Lesson 3: Currency - Calculating Currency Exchange

   Constructing Knowledge

When travelling abroad or watching television programs in other countries, you will see or hear items advertised in a different currency. It can be shocking to hear that a chocolate bar in Mexico costs 10 Pesos. The Peso is the Mexican equivalent of the Canadian dollar. However, because of exchange rates and the fact that currencies differ in value, a chocolate bar in Mexico does not cost $10 Canadian dollars.

One way to compare prices of items in different currencies is to convert one currency to the other.

Purchasing Exchange Rates for $1.00 Canadian Dollar
Foreign Currency Community Bank
United States Dollar $0.91
European Euro €0.66
Chinese Yuan ¥5.27
Mexican Peso $11.47

Ratios can be used to convert from one currency to another. One ratio will be the exchange rate obtained from the exchange rate chart. The other ratio will contain the variable you are trying to solve for any  given information.

\({\color{blue}{\frac{\$1\,\text{CAD}}{\$0.91\,\text{USD}}}}={\color{green}{\frac{\$100\,\text{CAD}}{y\,\text{USD}}}}\)

Notice that CAD is in the numerator for both ratios and that USD is in the denominator. To maintain equality, the units need to be placed consistently.

See the examples below for the algebraic steps used to solve for the unknown.

   Multimedia

A video describing the calculation of currency exchange is provided.


EXAMPLE 1

When shopping on the Internet, Sarah found similar items priced in different currencies. A tablet was listed for $419 in Canadian funds on one website. A similar tablet was found on an American website for $399 US funds. Which is the better deal?

Solution


Step 1: Set up the ratios.

For this example, the American tablet price will be changed to Canadian funds for comparison purposes.

When setting up the ratios, always put your unknown variable in the numerator (top number) of the fraction. This will make solving for the unknown easier.

\({\color{blue}{\frac{\$1\,\text{CAD}}{\$0.91\,\text{USD}}}}={\color{green}{\frac{y\,\text{CAD}}{\$399\,\text{USD}}}}\)

Step 2: Solve for the unknown value.

The first step is to multiply both sides by the denominator of the ratio which has the unknown value.

\(\begin{align} {\color{blue}{\frac{\$1\,\text{CAD}}{\$0.91\,\text{USD}}}}&={\color{green}{\frac{y\,\text{CAD}}{\$399\,\text{USD}}}} \\ \\ \frac{\$1\,\text{CAD}}{\$0.91\,\text{USD}}\times {\color{red}{\$399\,\text{USD}}}&=\frac{y\,\text{CAD}}{\cancel{\$399\,\text{USD}}}\times {\color{red}{\cancel{\$399\,\text{USD}}}} \\ \\ \frac{\$1\,\text{CAD}\times \$399\,\cancel{\text{USD}}}{\$0.91\,\cancel{\text{USD}}}&=y \\ \\ \$438.46\,\text{CAD}&=y \\ \end{align}\)

The tablet priced at $399.00 USD has a price of $438.46 CAD. As such, it would be better to purchase the tablet from the Canadian website (at this exchange rate).

EXAMPLE 2

A pair of high end basketball sneakers can be purchased for 600 yuan in China. What is the price in Canadian dollars (CAD)?

Solution


Step 1: Set up the ratios.

\({\color{blue}{\frac{\$1\,\text{CAD}}{5.27\,\text{Yuan}}}}={\color{green}{\frac{y\,\text{CAD}}{600\,\text{Yuan}}}}\)

Step 2: Solve for the unknown value.

\(\begin{align} {\color{blue}{\frac{\$1\,\text{CAD}}{5.27\,\text{Yuan}}}}&={\color{green}{\frac{y\,\text{CAD}}{600\,\text{Yuan}}}} \\ \\ \frac{\$1\,\text{CAD}}{5.27\,\text{Yuan}}\times {\color{red}{600\,\text{Yuan}}}&=\frac{y\,\text{CAD}}{\cancel{600\,\text{Yuan}}}\times {\color{red}{\cancel{600\,\text{Yuan}}}} \\ \\ \frac{\$1\,\text{CAD}\times 600\,\cancel{\text{Yuan}}}{5.27\,\cancel{\text{Yuan}}}&=y \\ \\ \$113.85\,\text{CAD}&=y \\ \end{align}\)

The basketball sneakers would cost $113.85 Canadian.


Now, it is your turn! Complete the questions in your Chapter 2, Lesson 3 Practice Makes Perfect that refer to Calculating Currency Exchange.



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