Deck 3: Ratios and Proportions

Question 1

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

Answer 1

= 2:3

Question 2

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

Answer 2

= 3:5:7

Question 3

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

Answer 3

= 3:2:1

Question 4

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

Question 5

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

Question 6

Express the following ratio in its lowest terms:

Question 7

Express the following ratio in its lowest terms:

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Express the following ratio in its lowest terms:

Question 14

Express the following ratio in its lowest terms:

Question 15

Express the following ratio in its lowest terms:

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

The cost to manufacture a fiberglass boat consists of $4480 for materials, $6330 for direct labour, and $2650 for overhead. Express the three cost components as a ratio.

Question 22

Solve the following proportion for the unknown quantity (3-figure accuracy): 9: 7 = 54:b

Question 23

Solve the following proportion for the unknown quantity (3-figure accuracy): 1.89: 0.31 = 175: k

Question 24

Solve the following proportion for the unknown quantity (3-figure accuracy): 1.56: h = 56.2: 31.7

Question 25

Solve the following proportion for the unknown quantity (3-figure accuracy): 0.057: 0.149 = z: 0.05

Question 26

Solve the following proportion for the unknown quantity (3-figure accuracy):

Question 27

Solve the following proportion for the unknown quantity (3-figure accuracy):

Question 28

Solve the following proportion for the unknown quantities (3-figure accuracy): 0.69: 1.17: 0.4 = r: s: 6.5

Question 29

Solve the following proportion for the unknown quantities:

Question 30

Last year, the U.S. sales of Ford, Toyota, and Hyundai, respectively, were in the ratio 92: 121: 35. Toyota 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 Hyundai?

Question 31

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 $66.3 million, and 635 full-time-equivalent teachers. The Middleton School District (MSD), with an annual budget of $52.1 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 enrollment as the provincial average?

Question 32

Kevin, Lyle, and Marnie operate Food Country as a partnership. Their agreement provides that half the profit in each calendar quarter 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 works in the business. The following table presents each partner's investment in the second column, and the hours worked (during the most recent quarter) in the third column. Rounded to the nearest dollar, how should the quarter's profit of $112,460 be allocated?

Question 33

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?

Question 34

Canada reported the following sales of alcoholic beverages in Ontario and Quebec for the year 2008. (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.

Question 35

Geological Consultants Ltd. is a private company with four shareholders: W, X, Y, and Z. Their respective shareholdings are shown in the table below. X is retiring and has come to an agreement with the other three shareholders to sell his shares to them for $175,000. The agreement calls for the 500 shares to be purchased and allocated among 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).

Question 36

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 37

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 38

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 39

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 40

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 41

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 42

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 43

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 44

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 45

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 46

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 47

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Question 48

Calculate each exchange rate in the third column of the following table using the alternative version of the exchange rate given in the second column.

Question 49

How much will it cost in Canadian dollars to purchase 2000 pesos in Mexican currency at a bank that charges a 3.5% commission on the transaction? Use an exchange rate of C$1.00 = Mexican peso 11.870

Question 50

How much will it cost (in Canadian funds) to purchase ≤2000 worth of traveller's cheques if the commission rate for this quantity of cheques is 0.5%?

Question 51

Keiko arrived in Oshawa to study English at Durham College. She used travellers' cheques totalling ×1,000,000 to open a Canadian dollar bank account. What will her opening balance be if the bank charges 0.5% for the currency conversion?

Question 52

Kevin lives in Calgary and wants to buy a 2003 Corvette. The best price he can find for a low-mileage model in Alberta is $49,000. (No GST would be payable on this private sale.) Through autotrader.com he tracked down a comparable car in California that he can purchase for US$34,500. To bring the car into Canada, he will have to pay 5% GST on the purchase price at Canada Customs. Additional costs will be C$287 for airfare to San Diego, US$350 in special transaction and documentation costs, and US$850 in travel and accommodation costs while driving the vehicle back to Calgary. How much will he save (in C$) by buying the Corvette in California?

Question 53

In April of 2007, Marielle bought 1200 shares of Yakamura Trading Co. on the Tokyo Stock Exchange at a price of ×1150 per share. The exchange rate at the time was ×105.04 per C$. She sold the stock for ×1310 per share in August of 2009 when the exchange rate was ×88.06 per C$. In Canadian dollars, how much did Marielle gain or lose on the investment?

Question 54

The above table presents the mid-rates, the Royal Bank's buy and sell rates, and ICE's buy and sell rates (at their Vancouver International Airport operation) on the same date for conversions between the Canadian dollar and three other major currencies.
a) As a percentage of the mid-rate, calculate to the nearest 0.01% the percent spread (between buy and sell rates) on US dollar conversions for each of the Royal Bank and ICE.
b) As a percentage of the mid-rate, calculate the percent buy-sell spread on British pound conversions for each of the Royal Bank and ICE.
c) As a percentage of the mid-rate, calculate the percent buy-sell spread on euro conversions for each of the Royal Bank and ICE.

Question 55

Based on the exchange rates in Problem 20, how many more British pounds can you obtain with C$2000 at the Royal Bank than at ICE? On any currency exchange transaction, ICE applies a C$3.50 service charge.

Question 56

Based on the exchange rates in Problem 20, how many more euros can you obtain with C$1500 at the Royal Bank than at ICE? On any currency exchange transaction, ICE applies a C$3.50 service charge.

Question 57

Based on the exchange rates in Problem 20, how many fewer Canadian dollars will you receive if you convert US$165 at ICE instead of at the Royal Bank? On any currency exchange transaction, ICE applies a C$3.50 service charge.

Question 58

Based on the exchange rates in Problem 20, how many fewer Canadian dollars will you receive if you convert €96 at ICE instead of at the Royal Bank? On any currency exchange transaction, ICE applies a C$3.50 service charge

Question 59

a) Based on the exchange rates in Problem 20, to the nearest 0.01%, what was the percent transaction cost on your purchase of ≤250 from each of the Royal Bank and ICE? On any currency exchange transaction, ICE applies a C$3.50 service charge.
b) You returned from your trip to Scotland with ≤16. Assuming the exchange rates remained the same, what percent transaction cost would you have paid to convert ≤16 back to C$ at the Royal Bank and at ICE?

Question 60

a) Based on the exchange rates in Problem 20, to the nearest 0.01%, what was the percent transaction cost on your purchase of €1100 from each of the Royal Bank and ICE? On any currency exchange transaction, ICE applies a C$3.50 service charge.
b) You returned from your trip to Italy with €53. Assuming the exchange rates remained the same, what percent transaction cost would you have paid to convert €53 back to C$ at the Royal Bank and at ICE?

Question 61

A cross-border shopping trip reveals that milk sells for US$4.39 per one-gallon jug versus C$5.49 per four-litre jug in Canada. Calculate the percent difference between Canada and the United States in the exchange rate-adjusted price of milk. Use the Canadian price as the base in the comparison. (1 U.S. gallon = 3.785 litres).

Question 62

Hamish and Grace MacDonald have been investigating the cost of a holiday in Britain. From their home in Welland, Ontario, it is equally inconvenient to fly out of Toronto or Buffalo, New York. On the Internet, they have found that they can fly Buffalo-London return on American Airlines for US$656 each, rent a hotel room in London for two people for one night at a cost of ≤87, and join Jolly Tours the next day for a two-week all-inclusive coach tour at a cost of ≤1150 per person. Alternatively, the MacDonalds can purchase an all-inclusive package (including a similar coach tour) from a local travel agent for C$3595 per person. Which alternative is cheaper? How much cheaper is it in C$ for two people?

Question 63

The price of a 40-ounce bottle of rum at a U.S. border duty-free store was US$24.95. At the same time, the price of a 750-mL bottle of similar quality rum in an Ontario LCBO was C$26.95. Using the Ontario price as the base, what is the percent saving (on the unit price) by buying rum at the duty-free store? (1 litre = 35.2 fluid ounces)

Question 64

A customized up-to-date Currency Cross Rate table (in the style of Table 3.2) may be created by using the Web site maintained by the OANDA Corporation. You can link to this site from the student textbook's Web site. Go to www.mcgrawhill.ca/olc/jerome/ and work your way to the page for the Student Edition. In the Student Edition's navigation bar, select "Chapter 3" in the drop-down box. In the list of resources for Chapter 3, select "Links in Student textbook" and then click on the link named "Create a Cross Rate Table." Hold down your CTRL key while selecting the currencies you want in the table. Then click on "Get my Table."
a) How many more or fewer C= will C$10,000 buy today than on the date in Table 3.2?
b) How many more or fewer ≤ will ×10,000 buy today than on the date in Table 3.2?

Question 65

If the number of ≤ per C$1.00 increases by 0.054 from the value C$1.00 = ≤0.55577, which currency has depreciated and by what percentage?

Question 66

If the number of C$ per × 1.00 decreases by 0.00054 from the value C$0.01137 = × 1.00, which currency has appreciated and by what percentage?

Question 67

If the C$ weakens by 0.5% relative to the €, C$1.00 = €.64491, what will be the new values for € per C$1.00 and C$ per €1.00?

Question 68

If the C$ strengthens by 1.2% relative to the US$ value, C$1.00 = US$0.92149, what will be the new values for US$ per C$1.00 and C$ per US$1.00?

Question 69

If the C$ appreciates (from the value C$1.7993 = ≤1.00) by C$0.0017 relative to the ≤, what will be the new value for ≤ per C$1.00?

Question 70

If the C$ weakens (from the value C$1.0852 = US$1.00) by C$0.0033 relative to the US$, what will be the new value for US$ per C$1.00?

Question 71

If the C$ strengthens by ≤0.0021 from the value C$1.00 = ≤0.55577, what will be the new value of C$ per ≤1.00?

Question 72

If the C$ weakens by €0.0211 from the value C$1.00 = €0.64491, what will be the new value of C$ per €1.00?

Question 73

If the C$ per US$ exchange rate decreases by C$0.005 from its value C$1.0852 = US$1.00), what will be the change in the US$ per C$ exchange rate?

Question 74

If the US$ per ≤ exchange rate increases by US$0.006 from its value US$1.00 = ₤1.6580, what will be the change in the ≤ per US$ exchange rate?

Question 75

If the × per A$ exchange rate increases by × 1 from its value × 1.00 = A$ = 80.413, what will be the change in the A$ per × exchange rate?

Question 76

If the € per × exchange rate decreases by €0.0007 from its value €1.00 = × .0073326, what will be the change in the × per €exchange rate?

Question 77

If the number of US$ per C$1.00 rises from 0.93452 to 0.94983, what will be the change in the C$ price to an importer of a US$1500 item?

Question 78

If the number of × per C$1.00 declines from 89.641 to 87.816, what will be the change in the C$ price to an importer of a × 195,000 item?

Question 79

If the number of ≤ per C$1.00 rises from 0.54182 to 0.55354, what will be the change in the C$ revenue from a foreign contract fixed at ≤23,000?

Question 80

If the number of US$ per C$1.00 declines from 0.94168 to 0.92679, what will be the change in the C$ price per ounce of gold which a Canadian gold mine sells at the international price of US$975 per ounce?