5. Review Exercises

Answers to the odd-numbered questions are available at the end of the book.

For problems 1 and 2, determine whether the given pairs of ratios are equivalent.

1. a. 6 : 8 and 18 : 24
   b. 30 : 25 and 36 : 48
   c. 10 : 35 and 14 : 49
   d. 24 : 30 and 12 : 18

2. a. 16 : 20 and 18 : 30
   b. 4 : 10 and 10 : 24
   c. 35 : 50 and 21 : 36
   d. 20 : 16 and 30 : 24

3. What is the ratio of a Canadian quarter (25¢) to a Canadian $5 bill, reduced to lowest terms?
4. What is the ratio of 12 minutes to 2 hours, reduced to lowest terms?
5. Ali can run 12 km in 40 minutes.
   1. Calculate his speed in km/hour.
   2. At this speed, how far can he run in 1.5 hours?
6. A car can travel 486 km using 45 litres of gas.
   1. Calculate the fuel efficiency of the car in km/litre.
   2. At this rate, how many litres of gas is required for a trip of 810 km?
7. Jeffrey and Gina were classmates who graduated together from college. Jeffrey found a job as a banker that pays him $189 for 9 hours and Gina found a job as a freelance artist that pays her $174 for 8 hours of work. Who is being paid a higher hourly rate and by how much?
8. Gregory purchased a racing motorbike, and Chris purchased a cruising motorbike. Jeffery travelled 765 km from Toronto to New York City in 8 hours and 20 minutes. Chris travelled 165 km from Toronto to Buffalo in 2 hours and 10 minutes. Based on this information, whose average speed was greater and by how much (in km/h)?
9. Which is the better buy based on the unit price: 360 grams for $2.99 or 480 grams for $3.75?
10. Which is the better buy based on the unit price: 125 grams for $4.75 or 175 grams for $5.95?

For problems 11 and 12, calculate the unit prices to determine which offer is best.

11. a. 3 kg of oranges for $7.99
    b. 4 kg of oranges for $9.99
    c. 5 kg of oranges for $11.99

12. a. 5 kg of rice for $4.99
    b. 8 kg of rice for $7.99
    c. 10 kg of rice for $9.49

13. If the ratio of sugar to flour in a pie is 3 : 5 and that of flour to eggs is 3 : 1, calculate the ratio of sugar : flour : eggs in the pie.
14. If the ratio of salespeople to marketing people in an organization is 5 : 4 and the ratio of marketing people to finance people is 5 : 2, what is the ratio of sales people : marketing people : finance people in the organization?

For problems 15 and 16, solve the proportion equations for the unknown value.

1. a. [latex]x : 9 = 26 : 39[/latex]
   b. [latex]16 : 24 = 12 : x[/latex]
   c. [latex]x : 0.45 = 0.16 : 1.20[/latex]

1. a. [latex]x : 15 = 24 : 36[/latex]
   b. [latex]8 : 14 = x : 35[/latex]
   c. [latex]12.5 : 70 = x : 1.4[/latex]

17. A car can travel 486 km using 45 litres of gas.
    1. Calculate the fuel efficiency of the car in km/litre.
    2. At this rate, how many litres of gas is required for a trip of 810 km?

18. A 450 gram loaf of bread costs $3.15 and has 15 slices.
    1. Determine the cost per 100 grams of bread..
    2. Determine the cost per slice of cheese.

19. The sales tax on an item costing $350.00 is $45.50. What will be the sales tax on an item costing $1,250.00?
20. Peter works 5.5 hours per day and his salary per day is $112.75. At this rate, how much will he receive if he works 7.5 hours per day?
21. Alexander, an investment banker, invests all his yearly earnings in stocks of high-tech, mining, and real-estate in the ratio of 4 : 5 : 3, respectively. Calculate his investment in mining stocks if his investment in high-tech stocks was $10,900.
22. The ratio of the driving distance from London to Hamilton, Mississauga, and Toronto is 3 : 4 : 5, respectively. If the distance from London to Hamilton is 125 km, calculate the distance from London to Mississauga and from London to Toronto.
23. Three college classmates, Khan, Thomas, and Lee decided to start a small business and invested $1,000, $2,500, and $3,500, respectively. If Lee decided to leave the business, how much would Khan and Thomas have to pay for Lee’s shares if they wanted to maintain their initial investment ratio?
24. Calvin decided to build a shopping complex with his two brothers, Kevin and Alex. They invested $200,000, $350,000, and $450,000, respectively. After the complex was built, Kevin decided to sell his share of the investment to Calvin and Alex. How much would each of them have to pay if they wanted to maintain the same ratio of their investments in the complex?
25. A, B, and C invested a total of $900 in the ratio of 3 : 4 : 5, respectively, to purchase a billiards table for their club house. After the table was delivered, each invested an additional $200 to purchase balls and cue sticks. Calculate their new investment ratio after their additional investments.
26. Samuel, his wife, and his mother jointly purchased an estate for $1,350,000. Their individual investments in the estate were in the ratio of 5 : 3 : 1 , respectively Each of them decided to invest an additional $250,000 to develop the estate into a small family resort. Calculate their new investment ratio after the additional investments.