Deck 3: Ratios and Proportions

Question 1

Express the following ratio in its lowest terms: 26:130:65

Answer 1

= 2:10:5

Question 2

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

Answer 2

= 8:3

Question 3

Express the following as an equivalent ratio whose smallest term is 1: 1.41: 8.22

Answer 3

1: 5.83

Question 4

Express the following ratio in its lowest terms: 11.7: 7.8: 3.9

Question 5

Express the following ratio in its lowest terms:

Question 6

Express the following ratio in its lowest terms: 12:64

Question 7

Express the following ratio in its lowest terms: 0.091: 0.021: 0.042

Question 8

Express the following ratio in its lowest terms:

Question 9

Express the following ratio in its lowest terms:

Question 10

Express the following ratio in its lowest terms:

Question 11

Express the following ratio in its lowest terms:

Question 12

Express the following as an equivalent ratio whose smallest term is 1: 7.6: 3

Question 13

Express the following as an equivalent ratio whose smallest term is 1: 0.177: 0.81

Question 14

Express the following ratio in its lowest terms: 0.08: 0.12

Question 15

Express the following ratio in its lowest terms:

Question 16

Express the following ratio in its lowest terms: 0.24: 0.39: 0.15

Question 17

Express the following ratio in its lowest terms: 0.84: 1.4: 1.96

Question 18

Express the following as an equivalent ratio whose smallest term is 1: 0.0131: 0.0086

Question 19

Express the following ratio in its lowest terms: 2.5: 3.5: 3

Question 20

Express the following ratio in its lowest terms: 45:15:30

Question 21

Express the following as an equivalent ratio whose smallest term is 1: 77:23:41

Question 22

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

Question 23

Express the following ratio in its lowest terms:

Question 24

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

Question 25

The instructions for preparing the fuel mix for a two-cycle engine are to add 250 ML of oil to 5 L of gasoline. What is the ratio (by volumes) of gasoline to oil in the fuel mix?

Question 26

Brine used in an industrial process is 12.5% salt by weight. What is the ratio (by weights) of salt to water in the brine?

Question 27

Express the following ratio in its lowest terms:

Question 28

Don, Bob, and Ron Maloney's partnership interests in Maloney Bros. Contracting are in the ratio of their capital contributions of $78,000, $52,000, and $65,000, respectively. What is the ratio of Bob's to Ron's to Don's partnership interest?

Question 29

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

Question 30

Solve the following proportions for the unknown quantities: t: 26: 10 = 24: 39: s

Question 31

During the last 3 months, Mako Distributing made 25% of its sales in Region A, 35% in Region B, and 40% in Region
C. What is the ratio of the sales in Region A to the sales in Region B to the sales in Region C?

Question 32

Victoria Developments has obtained $3.6 million of total capital from three sources. Preferred shareholders contributed $550,000 (preferred equity), common shareholders contributed $1.2 million (common equity), and the remainder was borrowed (debt). What is the firm's ratio of debt to preferred equity to common equity?

Question 33

Mark, Ben, and Tanya own 4,250; 2,550; and 5,950 shares, respectively, of MBT Inc. What is the ratio of their share holdings?

Question 34

The cost to manufacture a fiberglass boat consists of $2,240 for materials, $3,165 for direct labour, and $1,325 for overhead. Express the three cost components as a ratio.

Question 35

Express the following as an equivalent ratio whose smallest term is 1: 3.5: 5.4: 8

Question 36

Express the following ratio in its lowest terms:

Question 37

Express the following ratio in its lowest terms: 0.18: 0.60: 0.45

Question 38

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

Question 39

Express the following as an equivalent ratio whose smallest term is 1: 11:38:27

Question 40

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

Question 41

Solve the following proportion for the unknown quantity: 65: 43 = 27.3: x

Question 42

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?

Question 43

Solve the following proportion for the unknown quantity:

Question 44

Solve the following proportion for the unknown quantities: 3: 4: 13 = x: y: 6.5

Question 45

Solve the following proportion for the unknown quantity: 88: 17 = a: 45

Question 46

Solve the following proportion for the unknown quantity: 17: q = 119: 91

Question 47

A test-marketing of a newly released video in a representative Canadian city, with a population of 120,000, resulted in sales of 543 units in a 3-month period. If the video sells at the same rate in the rest of the country, where 21,000,000 Canadians have access to retail outlets, what 3-month sales may be forecast for the video?

Question 48

Solve the following proportion for the unknown quantity: 1.56: h = 56.2: 31.7

Question 49

Solve the following proportion for the unknown quantity: 0.043: y = 550: 198

Question 50

Last year, the U.S. sales of Ford, General Motors, and Chrysler, respectively, were in the ratio 92: 121: 35. GM has just announced sales of $10.8 billion for the first half of the current fiscal year. If the three companies have maintained the same market share as they had last year, what were the first half sales of Ford and Chrysler?

Question 51

Solve the following proportion for the unknown quantities: 1,410: 2,330: 870 = a: 550: b

Question 52

Solve the following proportion for the unknown quantity: 9: 7 = 54: b

Question 53

Solve the following proportion for the unknown quantities: 6: 7:5 = n: 105: m

Question 54

Solve the following proportion for the unknown quantity: d: 13.2 = 16: 31

Question 55

Solve the following proportion for the unknown quantities: 625: f: 500 = g: 3: 4

Question 56

Milan, Katka, and Shoshanna started their partnership with a total investment of $135,000 contributed in the ratio of 3: 4: 2. If each partner contributes another $10,000, what will be the ratio of their total contributions?

Question 57

An international equity mutual fund includes American stocks, Japanese stocks, German stocks, and British stocks in the ratio 27: 19: 14: 11, respectively. If its current holdings of German stocks are valued at $US238 million, what are the values of its holdings in the securities of the other three countries?

Question 58

Solve the following proportion for the unknown quantity:

Question 59

Solve the following proportion for the unknown quantity: 1.89: 0.31 = 175: k

Question 60

Solve the following proportion for the unknown quantity: 0.057: 0.149 = z: 0.05

Question 61

If you operate a home-based business, the Canada Revenue Agency (CRA) will usually allow you to report certain "office-in-home" expenses. The portion of heat, insurance, electricity, property taxes, and mortgage interest that you may report must be (in the language of the CRA) "reasonable under the circumstances." Rose uses 2 of the 11 rooms in her home for her real estate appraisal business. The combined floor area of the 2 rooms is 36 m². The remainder of the house has an area of 147 m². Rose's total expenses in the home-related categories were $17,512 for the year. What amount will qualify as "office-in-home" expenses if the proration is based on:
a) The number of rooms used for the business?
b) The floor area devoted to business use?

Question 62

The Ministry of Education reported that the average school district in the province has 13,450 students in "K to 12" programs, an annual budget of $87.4 million, and 635 full-time-equivalent teachers. The Middleton School District (MSD), with an annual budget of $69.1 million and 498 teachers, serves 10,320 students. What adjustments would have to be made to MSD's budget and staffing to have them in the same proportion to enrolment as the provincial average?

Question 63

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?

Question 64

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?

Question 65

Solve the following proportion for the unknown quantities: a: 58: 132 = 38: 27: b

Question 66

Their partnership agreement requires Harry, Draco, and Hermione to provide capital "when and as required" by the partnership in the ratio 1: 1.35: 0.85, respectively.
a) The total initial capital requirement was $256,000. How much did each partner contribute?
b) One year later, Hermione's share of an additional injection of capital was $16,320. What was Draco's share?

Question 67

When real estate is sold, the year's property taxes are allocated to the vendor and the purchaser in proportion to the number of days that each party owns the property during the year. If the purchaser took possession of a property effective August 8 (of a 365-day year), how will the year's property taxes of $2,849 be allocated to the vendor and purchaser?

Question 68

Three insurance companies agree to jointly insure a cargo ship for $38.6 million. If insurers A, B, and C allocate premiums received and accept the risk in the ratio 3: 8: 5, respectively:
a) How will the annual premium of $900,000 be distributed?
b) What is the maximum claim exposure of each insurer?

Question 69

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

Question 70

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.

Question 71

A partnership agreement provides that half of the annual profit be distributed in proportion to each partner's investment in the partnership, and that the other half be distributed in proportion to the total number of hours that each partner worked in the business during the year. How should the most recent year's profit of $84,780 be allocated if the amounts invested by Huey, Dewey, and Louie are $70,000, $30,000, and $45,000, and their hours of work for the year were 425; 1,680; and 1,440, respectively?

Question 72

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?

Question 73

Wendy, Simone, and Leif share the costs of their coffee fund in the ratio . How will $50 be allocated among them?

Question 74

How should common area costs totalling $28,600 be allocated among commercial tenants A, B, C, and D if the costs are prorated based on leased areas of 1,260; 3,800; 1550 and 2,930 sq ft, respectively?

Question 75

The new University Hospital is scheduled to have 436 beds. The ratio of nurses to beds to nurses' aides for staffing the hospital is 4: 9: 2. How many nurses and aides will need to be hired?

Question 76

A provincial government allocates 29% of its budget to education, 31% to health care, and 21% to social services. If the dollar amount budgeted for education is $13.7 billion, how much is budgeted for health care and for social services?

Question 77

Mr. Subhani's will specified that, upon liquidation of any asset, the proceeds be divided among his wife, his son, and his sister in the ratio of 7: 5: 3.
a) If the son received $9500 from the sale of securities, what amounts did Bartlett's wife and sister receive?
b) What amount would the sister receive from the sale of the deceased's boat for $27,000?

Question 78

Solve the following proportion for the unknown quantities: 8500: x: y = 4/3: 1: 5/3

Question 79

If you use your car for both business and pleasure, the Canada Revenue Agency will usually allow you to report a portion of the costs of operating the vehicle as a business expense. This portion is determined by the ratio of the distance travelled on business to the total distance travelled in the year.
Last year, Harjap spent a total of $11,348 on gasoline, oil, repairs and maintenance, and insurance. His travel log shows that he drove 14,488 km on business and 8,329 km on personal use. What vehicle expense can Harjap report for the year?

Question 80

For the last 5 years the sales of Departments D, E, and F have maintained a relatively stable ratio of 13: 17: 21. Department E is forecasting sales of $478,000 for next year. Based on the past sales ratio, what sales would be expected for Departments D and F?