Chapter 1 | Ratios, Proportions, Percents, and Applications
1.5 |
Currency Conversions
A very common application of proportions is the conversion of currencies between different countries.
Exchange Rates
Exchange rates:
used to convert
currencies between
countries.
The exchange rate, also called the foreign exchange rate or forex rate, is used to convert currencies
between countries. Therefore, knowing the exchange rate would allow you to calculate the amount
of a currency required to purchase one unit of another currency.
For example, to convert Canadian currency to US currency, it is important to know how many
Canadian dollars are equivalent to one US dollar, or vice versa.
The value of a currency may fluctuate constantly during the day and the exchange rate may vary
accordingly. For example, at 12:00 pm EST on January 27, 2014, US$1 was equal to C$1.1101
and C$1 was equal to US$0.9007. Therefore, the exchange rate on that date and time was US$1 =
C$1.1101 and C$1 = US$0.9007.
Currency Cross-Rate Table
Currency exchange rates are generally displayed in a table called the currency cross-rate table for
quick reference.
Exchange rates given in the currency cross-rate table below are as on January 27, 2014 at 5:00 pm EST.
Table 1.5(a)
Currency Cross-Rate Table, as of January 27, 2014
(One unit of)
Symbol
C$
US$
€
£
¥
CHF
A$
Canadian dollar: C$
US dollar: US$
Euro: €
British pound: £
Japanese yen: ¥
Swiss franc: CHF
Australian dollar: A$
C$
1.0000
1.1115
1.5198
1.8431
0.010838
1.2401
0.9712
US$
0.8996
1.0000
1.3673
1.6584
0.009750
1.1153
0.8739
€
0.6579
0.7313
1.0000
1.2128
0.007130
0.8158
0.6391
£
0.5425
0.6029
0.8244
1.0000
0.00587
0.6726
0.5270
¥
92.2677
102.5570
140.239
170.099
1.0000
114.452
89.6563
CHF
0.8063
0.8965
1.2257
1.4865
0.008737
1.0000
0.7832
A$
1.0295
1.1442
1.5645
1.8974
0.011153
1.2766
1.0000
(Equivalent to)
Common currencies
and their symbols
The vertical column of the table represents one unit of the currency to be converted and the
horizontal rows represent the equivalent value of it in another currency.
For example, US$1 = C$1.1115 and £1 = CHF1.4865.
Based on the exchange rates given in Table 1.5(a), the exchange rates of foreign currencies in
Canadian dollars and vice versa are given in Table 1.5(b) for easy reference.
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Chapter 1 | Ratios, Proportions, Percents, and Applications
Table 1.5(b)
Exchange Rates of Foreign Currencies per Canadian dollar and Vice Versa
Foreign Currency
Symbol
US dollar
Units per C$
C$ per Unit
US$
1.1115
0.8996
Euro
€
1.5198
0.6579
British pound
£
1.8431
0.5425
Japanese yen
¥
0.010838
92.2677
CHF
1.2401
0.8063
A$
0.9712
1.0295
Swiss franc
Australian dollar
For calculations involving conversion from one currency to another, we will either use the
cross-reference table or exchange rates provided in the question. We will be using the method of
proportions to solve examples that follow.
Example 1.5(a)
Currency Conversion from Canadian Dollar to US Dollar
Based on the exchange rates provided in Table 1.5(a) (Currency Cross-rate Table), how many US
dollars will you receive when you convert C$400?
Solution
From the cross-rate table, US$1.00 = C$1.1115
US$ : C$ = US$ : C$
1.00 : 1.1115 = x : 400.00
US$
C$
1.00
1.1115
x
400.00
In fractional form, 1.00 = 1.1115 Or
x
400.00
x
1.00 =
1.1115 400.00
Cross-multiplying, x = 400.00 = 359.874044... = US$359.87
1.1115
Therefore, you will receive US$359.87 when you convert C$400.00.
Example 1.5(b)
Currency Conversion from C$ to US$ and from US$ to C$
If US$1 = C$1.1115, then (i) how much will you receive if you convert US$1000 to Canadian
dollars and (ii) how much will you receive if you convert C$1000 to US dollars?
Solution
(i) US$ : C$ = US$ : C$
1.00 : 1.1115 = 1000.00 : x
US$
C$
1.00
1.1115
1000.00
x
1000.00
1.00
In fractional form, 1.00 = 1.1115 Or 1.1115 = x
1000.00
x
Cross-multiplying and solving,
x = C$1111.50
Therefore, you will receive C$1111.50 when you convert US$1000.00.
Chapter 1 | Ratios, Proportions, Percents, and Applications
Solution
continued
29
US$ : C$ = US$ : C$
1.00 : 1.1115 = x : 1000.00
US$
C$
1.00
1.1115
x
1000.00
In fractional form, 1.00 = 1.1115
x
1000.00
x
1.00
Or 1.1115 = 1000.00
Cross-multiplying and solving, x = 899.685110... = US$899.69
Therefore, you will receive US$899.69 when you convert C$1000.00.
Example 1.5(c)
Converting from One Currency to Another Currency, Given Exchange Rates
Samantha is travelling from Canada to London on vacation. If £1 = C$1.8431 then how much will
she receive if she converted C$1000 to British pounds?
Solution
£ : C$ = £ : C$
1.00 : 1.8431 = x : 1000.00
£
C$
1.00
1.8431
x
1000.00
In fractional form, 1.00 = 1.8431 Or
x
1000.00
x
1.00 =
1.8431 1000.00
Cross-multiplying and solving, x = 542.564158... = £542.56
Therefore, she will receive £542.56 when she converts C$1000.00.
Example 1.5(d)
Series of Currency Conversions
If US$1 = C$1.1115 and C$1 = A$1.0295, calculate the amount of US dollars you will receive
with 100 Australian dollars.
Solution
First, find out how many Canadian dollars you can get with A$100.
C$ : A$ = C$ : A$
1.00 : 1.0295 = x : 100.00
C$
A$
1.00
1.0295
x
100.00
In fractional form, 1.00 = 1.0295
x
1000.00
Cross-multiplying and solving,
Or
1.00 = x
1.0295 100.00
x = C$97.134531...
Now, find out how many US dollars you can get with C$97.134531...
US$ : C$ = US$ : C$
1.00 : 1.1115 = x : 97.134531...
US$
A$
1.00
1.1115
x
97.134531
x
In fractional form, 1.00 = 1.1115
Or 1.00 =
x
97.134531
97.134531...
1.1115
Cross-multiplying and solving, x = 87.390491... = US$87.39
Therefore, you will receive US$87.39 when you convert A$100.00.
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Chapter 1 | Ratios, Proportions, Percents, and Applications
Example 1.5(e)
Series of Currency Conversions and Converting Back to the Original Currency
Martha, a globe trotter, traveled from Canada to the US with C$3000 as backup cash. In the
US, she converted this amount to US dollars. From there, she traveled to Japan. While in Japan,
she converted her US dollars to Japanese yen. She finally returned to Canada and converted the
Japanese yen to Canadian dollars.
(i) How many US dollars did she have as backup cash during her stay in the USA?
(ii) How many Japanese Yen did she have while she was in Japan?
(iii)Check to see if she received her original amount of C$3000 when she converted her
Japanese Yen back to Canadian dollars.
Use these exchange rates: C$1 = US$0.8996, US$1 = ¥102.5570, and C$1 = ¥92.2677.
Solution
(i) How many US dollars did she have as backup cash during her stay in the USA?
C$ : US$ = C$ : US$
1.00 : 0.8996 = 3000.00 : x
C$
US$
1.00
0.8996
3000.00
x
In fractional form, 1.00 = 0.8996
x
3000.00
Or
1.00 = 3000.00
0.8996
x
x = US$2698.80
Cross-multiplying and solving,
Therefore, she had US$2698.80 in the USA.
(ii) How many Japanese yen did she have while she was in Japan? US$ : ¥ = US$ : ¥
1.00 : 102.5570 = 2698.80 : x
US$
¥
1.00
102.5570
2698.80
x
1.00
In fractional form, 1.00 = 102.5570 Or
= 2698.80
102.5570
x
x
2698.80
Cross-multiplying and solving, x = 276,780.8316... = ¥276,780.83
Therefore, she had ¥276,780.83 in Japan.
(iii)Check to see if she received her original amount of C$3000.00 when she converted her
Japanese yen back to Canadian dollars. C$ : ¥ = C$ : ¥
1.00 : 92.2677 = x : 276,780.83
C$
¥
1.00
92.2677
92.2677
276,780.83
In fractional form, 1.00 = 92.2677
x
276,780.83
Or
x
1.00 =
92.2677 276,780.83
Cross-multiplying and solving, x = 2999.76... = C$2999.76
Therefore, she would receive C$3706.70 in Canada.
Note: The slight difference of C$0.24 is because of rounding every time she converts a currency.
Chapter 1 | Ratios, Proportions, Percents, and Applications
1.5 |
Exercises Answers to odd-numbered problems are available online
1. How much would you receive if you convert the following:
a. CHF200 to British pounds (£)
b. C$3000 to US dollars (US$)
c. US$5000 to Canadian dollars (C$)
d. £10 to Canadian dollars (C$)
Assume that the current exchange rates are:
£1 = CHF1.4865, US$1 = C$1.1115, £1 = C$1.8431
2. How much would you receive if you convert the following:
a. C$18,000 to Japanese yen (¥)
b. US$2850 to Swiss francs (CHF)
c. £18 to Swiss francs (CHF)
d. CHF850,935 to Canadian dollars (C$)
Assume that the current exchange rates are:
¥1 = C$0.010838, CHF1 = US$1.1153, £1 = CHF1.4865, CHF1 = C$1.2401
3. If C$1 = £0.5425 and £1 = US$1.6584, how many Canadian dollars will you receive with US$1000?
4. If C$1 = ¥92.2677 and ¥1 = US$0.009750, how many Canadian dollars will you receive with US$1000?
5. If £1 = US$1.6584 and A$1 = US$0.8739, determine the exchange rate for one Australian dollar to British pounds.
6. If €1 = ¥140.239 and C$1 = ¥92.2677, determine the exchange rate one for Canadian dollar to Euro.
7. Suppose the exchange rate changes from C$1 = A$1.0295 to C$1 = A$1.1385, what will be the change in the value
of a machine in Australian dollars if it costs C$3000?
8. Suppose the exchange rate changes from C$1 = £0.5425 to C$1 = £0.6245, what will be the change in the value
of a printer in British pounds if it costs C$280?
9. Bernie, a senior sales representative at a multinational company, travelled from Canada to Japan via the UK. He
left Canada with C$8000. When he reached the UK he converted all his cash to British pounds. The conversion rate
was £1 = C$1.8431. After spending £1000, he left for Japan where he converted the remaining British pounds to
Japanese yen at an exchange rate of ¥1 = £0.005878. He spent ¥125,400 in Japan and finally returned to Canada.
Based on the information in this question, calculate the number of Canadian dollars he received when he converted
the remaining Japanese yen to Canadian dollars.
10. Kristin saved up C$3000 to use for her travels during her summer holidays. She first travelled from Toronto
to Switzerland, where she converted all her Canadian dollars to Swiss francs at an exchange rate of
C$1 = CHF0.8063. She spent CHF1452 and then travelled to London, where she converted the remaining Swiss
francs to British pounds at an exchange rate of CHF1 = £0.6726. She spent £570.34 in London before returning to
Toronto. How many Canadian dollars did she receive when she converted the remaining British pounds to Canadian
dollars?
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