Exam 3: Ratios and Proportions

Jane, Lynda, and Ginny run a consignment dress store. The partnership agreement states that the profits are distributed according to the hours each works in the store. For the month of July, profits are $8,500. The hours worked by Jane, Lynda and Ginny are 170, 190, and 200 respectively. How should the month's profits be allocated?

Sam, Sue, and Cliff formed a partnership in the ratio of 1:.80:1.25. If Sue's contribution was $32,000, how much did Sam and Cliff contribute?

Express the following as an equivalent ratio whose smallest term is 1: 0.47: 0.15: 0.26

Canada reported the following sales of alcoholic beverages in Ontario and Quebec for a particular year. (All figures are in $ millions.) If Ontarians had allocated their total expenditures on alcoholic beverages in the same proportion as Quebecers, a) How much more would they have spent on wine? b) How would their expenditure on beer have differed? Round both answers to the nearest $0.1 million.

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?

Tom Nortons Donuts considers the Hamilton area to be its most mature, fully-exploited market. The 59 outlets in the metropolitan area serve a population of 675,000 and generate annual sales of $66.67 million. The management of Tom Nortons views its Calgary market as under-exploited. The 65 outlets generate annual sales of $63.05 million from a population of 1,075,000. If Tom Nortons had penetrated the Calgary market to the same degree and success as the Hamilton market, how many additional outlets would it have, and how much higher (rounded to the nearest $0.01 million) would its annual sales be?

To gain an impression of how important and how widespread is the use of ratios in business and finance, see how many million matches you get when you "Google" on the key words: (i) "financial"AND "ratio OR ratios," (ii) "business"AND "ratio OR ratios."

A punch recipe calls for fruit juice, ginger ale, and vodka to be mixed in the ratio 6: 2.5: 1. How much fruit juice and vodka should be mixed with a 2 litre bottle of ginger ale?

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

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?

Kristina, Larissa, and Marika invested $50,000, $80,000 and $100,000 respectively in a fashion retail business. They decided to expand the store and needed an extra $75,000. How much of the $75,000 should each invest in order to maintain the same proportion?

The current exchange rates show that US$1.00 = €0.7700. If you have $600 US dollars, what is the equivalent amount in euros?

Three partners invest in a business in the ratio of 30%, 25%, and 45%. How should the most recent quarter's profit of $73,800 be distributed?

Victoria is going to ask for a raise. Over the past year, the CPI has gone from 119.6 to 122.6. Victoria now earns $45,000. What is the minimum raise that Victoria should ask for in order to maintain the same buying power?

Geological Consultants Ltd. is a private company with four shareholders - W, X, Y, and Z - owning 300, 500, 350, and 400 shares, respectively. X is retiring and has come to an agreement with the other three shareholders to sell his shares for $175,000. The agreement calls for the 500 shares to be purchased and allocated to W, Y, and Z in the same ratio as their present shareholdings. The shares are indivisible, and consequently the share allocation must be rounded to integer values. a) What implied value does the transaction place on the entire company? b) How many shares will W, Y, and Z each own after the buyout? c) What amount will each of the continuing shareholders contribute toward the $175,000 purchase price? Prorate the $175,000 on the basis of the allocation of the shares in part b.

Aaron, Luc and Isaac invested in a business in the ratio of 3.5: 5: 7.5. The factory that they leased requires renovations of $125,000. If the partners want to maintain their investments in the business in the same ratio, how much should each partner pay for the renovations?

A business consultant is analyzing the cost structure of two firms in the same retail business. On sales of $3.66 million, Thrifty's had wholesale costs of $2.15 million and overhead expenses of $1.13 million. If Economart had the same proportionate costs on its sales of $5.03 million, what would its wholesale costs and overhead expenses have been?

Solve the following proportion for the unknown quantity:

The following table shows National Paper Products' capital investment in each of its three divisions, and the most recent year's gross sales for each division. The operating costs of the head office for the year were $839,000. These costs are allocated to the divisions before each division's profit is determined. How much should be allocated to each division if the costs are prorated on the basis of: a) The capital investment in each division? b) The sales of each division?

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?