Exam 3: Ratios and Proportions

Calculate the missing quantities in the following problems to four-figure accuracy:

The CPI increased from 125.0 to 132.0 over a three-year period. If a person earned $40,000 at the beginning of the three-year period, how much would they have to earn at the end of the three-year period to maintain the same purchasing power?

A manufacturing business currently employs 10 managers, 550 assembly line workers, and 140 support staff. The business is expanding, and expects to add 175 assembly line workers. Assuming the same proportions, how many more managers and support staff should be hired?

If the C$ weakens by 1% relative to the euro (C$1.00 = €0.7448), what will be the new value for the euro per C$1.00?

Solve the following proportion for the unknown quantity: 0.043: y = 550: 198, to four decimal places.

A bartenders' handbook recommends that one bottle of spirits be provided per 10 guests at a New Year's Eve party. Furthermore, the relative consumption of scotch, rye, and rum is in the ratio of 3: 5: 4. How many bottles of each liquor should be stocked for a party expecting 480 guests?

From the end of 2014 until the end of 2016, the S&P/TSX Composite Index rose from 8934 to 12,434. If you had invested $50,000 in a portfolio of the shares of the companies in the Index at the end of 2014, what would the value of those shares have been at the end of 2016? (This calculation considers only the price appreciation of the original shares. It does not include the portion of the growth in the portfolio's value resulting from the receipt and reinvestment of dividends.)

Analysis of Suzanne's sales, showed 12% in the West Region, 36% in the North Region, 6% in the South Region and the 46% in the East Region. The ratio of sales expressed in its smallest term is 2:6:1:2.67

Solve the following proportion for the unknown quantities: 0.69: 1.17: 0.4 = r: s: 6.5

The CPI in 2005 was 113.5 and in 2012 was 125.6 if compared to the base year of 2000, the purchasing power of the Dollar in 2012 was 88.11% of 2000.

Express the following ratio in its lowest terms: 56:21

A provincial government budget forecasts expenditures of $10.4 billion on education, $9.1 billion on health services, and $6.6 billion on social services. Express the three budget items as a ratio without decimals, in lowest terms.

Last year, a company's salespersons, A, B, and C recorded sales as follows: "A" recorded three sevenths (3/7) of the total, "B" recorded one quarter (1/4) of the total and "C" recorded the rest of the sales. Express, in lowest terms, the sales ratio of A: B:C.

Based on past experience, a manufacturing process requires 2.3 hours of direct labour for each $174 worth of raw materials processed. If the company is planning to consume $78,300 worth of raw materials, what total amount should it budget for labour at $31.50 per hour?

Connie's neighbour sold 14.5 hectares of raw land for $128,000. If Connie were to sell her 23.25 hectare parcel at a proportionate price, what amount would she receive?

The leases in multiple-unit commercial developments commonly permit the landlord to allocate to the tenants various common area and general costs such as property taxes, janitorial services, security services, and snow removal. These costs are usually prorated on the basis of the floor area leased to each tenant. Granny's Chicken, Toys 'n Novelties, and Pine Tree Pharmacy are the three tenants in Pine Tree Square. They lease 172 square metres, 136 square metres, and 420 square metres, respectively. How should common costs totalling $9,872 for the past year be allocated?

The price of a laser printer dropped from $299.99 to $175. What index number would represent the change in price?

Three partners share the partnership's profit according to the proportion of the business each owns. Ms. A owns 30%, Mr. B owns 25% and Ms. C owns the remainder. What profit would Mr. B receive if Ms. A receives $32,500?

Sam, Domenic, and Sal invested $200,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

Carol bought 25.5 hectares of land for $63,000. If she buys another 80 hectares of land at the same price per hectare as her first purchase, how much must she pay for her second purchase?