Explore all topics
Start Free Trial
Need Help? Contact us
back arrowfull exam logo
search
ai logoChat with AI
Servicesarrow
Discoverarrow

Topics

Explore all topics
Discover more topics
expand icon
book Business Mathematics 13th Edition by Gary Clendenen,Stanley Salzman cover

Business Mathematics 13th Edition by Gary Clendenen,Stanley Salzman

Edition 13ISBN: 978-0321955050
book Business Mathematics 13th Edition by Gary Clendenen,Stanley Salzman cover

Business Mathematics 13th Edition by Gary Clendenen,Stanley Salzman

Edition 13ISBN: 978-0321955050
Exercise 2
GENERAL MOTORS
www.Gm.com
Facts:
• 1908: Founded
• 1982: Built huge factory in Spain
• 2009: Files for bankruptcy
• 2010: Emerges from bankruptcy
• 2013: Over 200,000 employees GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries.
Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered.
Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.)
Writing Ratios
Write a ratio in the form GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____ for each word phrase. Notice in each example that the number mentioned first is always the numerator.
SOLUTION
(a) The ratio of 5 hours to 3 hours is GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(c) The ratio of $700,000 in sales to $950,000 in sales is written this way. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Reduce to write this ratio in lowest terms. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Writing Ratios GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Burger King sold the following items in a one-hour period last Friday afternoon.
70 bacon cheeseburgers
15 plain hamburgers
30 salad combos
45 chicken sandwiches
40 fish sandwiches
Write ratios for the following items sold:
(a) bacon cheeseburgers to fish sandwiches
(b) salad combos to chicken sandwiches
(c) plain hamburgers to salad combos
(d) fish sandwiches to total items sold
SOLUTION
(a) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(b) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(c) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(d) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Determining If a Proportion Is True
Decide whether the following proportions are true.
(a) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(b) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
SOLUTION
(a) Find each cross product. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Since the cross products are equal, the proportion is true.
QUICK TIP
The symbol ? means "not equal to."
(b) Find the cross products. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
This proportion is false, so GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Solving a Proportion
Find the value of the unknowns. Use the first method for (a) and the second method for (b).
(a) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(b) GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
SOLUTION
(a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
(b) Solve for the unknown using the method of cross products. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Solving Proportions GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce?
SOLUTION
Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Now substitute the given information. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Use the cross-products to solve the proportion. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
The 5 crates cost $138.33.
Solving Applications GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm.
SOLUTION
Let x represent the cost to the Thailand firm, then GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
The Thailand firm's share of the costs is $3,525,000.
Solving Applications
James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
SOLUTION
Set up a proportion in which the height of the tree is given the variable name x. GENERAL MOTORS www.Gm.com Facts: • 1908: Founded • 1982: Built huge factory in Spain • 2009: Files for bankruptcy • 2010: Emerges from bankruptcy • 2013: Over 200,000 employees In some respects, General Motors (GM) is the story of globalization. It was one of the most successful companies in the world in the 1960s under the gifted manager Alfred Sloan. As it expanded globally, some of the jobs that had gone to Americans were moved overseas, partly to be closer to where vehicles were sold but also to cut costs. Labor costs were much lower in other countries. Gasoline prices increased sharply during the 1970s and many Americans turned away from GM products and bought cars from Toyota, Honda, or Nissan. Americans were interested in the smaller, high-quality cars built by the Japanese. The weakened state of GM and the financial crisis of 2008-2010 forced the company to file for bankruptcy in 2009 when the U.S. government stepped in to help. But the company has since recovered. Ben James received a bachelor's degree in statistics and a master's degree in business administration. He has worked at GM for several years. Among other things, he studies data such as that shown in the following two figures and develops equations to forecast demand. Many factors are involved in making a forecast. To illustrate, use the following equation to make a monthly forecast of car sales (in thousands) in one area given Advertising = $6.2 (millions), Economic Growth = 2.8, (.028), and Level of Competition =.6. (See Section, Examples 1-8.) Writing Ratios Write a ratio in the form for each word phrase. Notice in each example that the number mentioned first is always the numerator. SOLUTION (a) The ratio of 5 hours to 3 hours is (b) To find the ratio of 5 hours to 3 days, first convert 3 days to hours. Since there are 24 hours in 1 day, 3 days = 3 · 24 = 72 hours. Then the ratio of 5 hours to 3 days is the quotient of 5 and 72. (c) The ratio of $700,000 in sales to $950,000 in sales is written this way. Reduce to write this ratio in lowest terms. Writing Ratios Burger King sold the following items in a one-hour period last Friday afternoon. 70 bacon cheeseburgers 15 plain hamburgers 30 salad combos 45 chicken sandwiches 40 fish sandwiches Write ratios for the following items sold: (a) bacon cheeseburgers to fish sandwiches (b) salad combos to chicken sandwiches (c) plain hamburgers to salad combos (d) fish sandwiches to total items sold SOLUTION (a) (b) (c) (d) Determining If a Proportion Is True Decide whether the following proportions are true. (a) (b) SOLUTION (a) Find each cross product. Since the cross products are equal, the proportion is true. QUICK TIP The symbol ? means not equal to. (b) Find the cross products. This proportion is false, so Solving a Proportion Find the value of the unknowns. Use the first method for (a) and the second method for (b). (a) (b) SOLUTION (a) Solve for the unknown by multiplying both sides of the equation by the product of the denominators. (b) Solve for the unknown using the method of cross products. Solving Proportions A food wholesaler charges a restaurant chain $83 for 3 crates of fresh produce. How much should it charge for 5 crates of produce? SOLUTION Let x be the cost of 5 crates of produce. Set up a proportion with one ratio the number of crates and the other ratio the costs. Use this pattern. Now substitute the given information. Use the cross-products to solve the proportion. The 5 crates cost $138.33. Solving Applications A firm in Hong Kong and one in Thailand agree to jointly develop an engine-control microchip to be sold to North American auto manufacturers. They agree to split the development costs in a ratio of 8:3 (Hong Kong firm to Thailand firm), resulting in a cost of $9,400,000 to the Hong Kong firm. Find the cost to the Thailand firm. SOLUTION Let x represent the cost to the Thailand firm, then The Thailand firm's share of the costs is $3,525,000. Solving Applications James McIntosh wants to cut a tree down in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree. SOLUTION Set up a proportion in which the height of the tree is given the variable name x. The height of the tree is 25.5 feet. Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
The height of the tree is 25.5 feet.
Sales = 34.8 + 5.3 Advertising + 485 Economic Growth ? 34.2 Level of Competition _____
Explanation
Verified
like image
like image
like image

Monthly forecast of car sales in one are...

close menu
Business Mathematics 13th Edition by Gary Clendenen,Stanley Salzman
cross icon

Why don’t you like this exercise?

Other
Minimum 8 character and maximum 255 character
Character 255
Examlex
Examlex
Work With Us
Policies
Download the App
Scan to downloadDownload the App
qr-code
Links
Links
Work With Us
Download the App

Scan to downloadDownload the App
qr-code

Copyright © 2026 Examlex LLC.
  • facebook-footer
  • instagram-footer
  • x-footer
  • tiktok
  • Linktree