Exam 3: Ratios and Proportions

Solve for X in the proportion: 3: 5 = X: 20

If the C$ weakens by 2½% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

A manufacturing business currently employs 8 managers, 147 sales staff, and 7 IT staff. The business is expanding, and expects to add another 18 sales staff. Assuming the same proportions, how many more managers and IT staff should be hired?

The exchange rate between Currencies X and Y is currently Y0.05614 = X1.00. If X weakens by 1.5% relative to Y, what will be the new values for the exchanges rates per unit of X and per unit of Y?

A three-year magazine subscription costing $120 is cancelled after fifteen months. The company has a policy to refund any remaining monthly issues minus a $25 cancellation fee. What refund should the company pay?

Using the exchange rates in Table 3.2, show that you will receive as many euros for C$1150 by first converting the dollars to pounds and then converting the pounds to euros, as you would by converting the dollars directly to euros.

Express the following ratio as an equivalent ratio whose smallest term is 1. 0.75: 3

If the C$ strengthens by 1% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

Sam and his sister shared an inheritance from their aunt in the ratio of 4:5 respectively. Sam's share was $21,000. What was his sister's share?

A province's Ministry of Social Services has found that both the number of people receiving social assistance and the province's total expenditures on social assistance are proportional to the rate of unemployment. Last August when the provincial unemployment rate was 8.4%, the province provided benefits to 89,300 individuals at a cost of $107.4 million. The forecasted unemployment rate for next August is 7.9%. How many people can the province expect to need social assistance next August? What amount should the province budget for social assistance in August?

A three-year magazine subscription costing $136 may be cancelled at any time, and a prorated refund will be made for the remaining weekly issues. If Juanita cancels her subscription after receiving 17 issues in the second year, what refund should she get? Assume there are exactly 52 weeks in a year.

Sam, Domenic, and Sal invested $100,000, $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?

Heinz returned from a holiday in Germany with €235. How much will he receive from his bank when he converts the currency back to Canadian dollars? The bank charges a 1.6% service charge for the transaction.

Marion took orders for gift-wrapping packages at Christmas. Of the 2,080 orders, 45% of customers preferred red paper and ribbon, 30% preferred green, and 25% preferred blue or white. What is the ratio of sales for red, green and blue or white gift-wrapping packages in lowest terms?

If the C$ strengthens by £0.0021 from the value C$1.00 = £0.6370, what will be the new value of C$ per £1.00?

Tomiko is planning a trip from Japan to Canada and then to the United States. She intends to bring ¥300,000 and converting it to Canadian Dollars. She plans to spend approximately ¾ of her money in Canada and the remaining in the United States. Using the information from Table 3.2 and disregarding any commission, she should have approximately US621.46 remaining to spend in the US. TABLE 3.2 Currency Cross Rates (noon, Toronto, October 30, 2015) Source: Bank of Canada

The Mississauga plant of a pharmaceutical distribution company handled 2,750,000 cases of products during the last year, while the Brampton plant handled 2,250,000 cases. How will overhead costs of $2,500,000 for the year be allocated between the two plants if based on the number of cases handled?

An industrial process requires a mixture of 16% chlorine to alcohol by weight. The ratio of alcohol to chlorine is also 16% by weight.

Solve the following proportion for the unknown quantity: $m: \frac{3}{4}=\frac{1}{2}: \frac{9}{8}$ Leave your solution in fraction form.

Express the following ratio in its lowest terms: $\frac{9}{8}: \frac{3}{4}: \frac{3}{2}$