 # How Currency Exchange Works

When you are abroad, it’s important to know how much the country’s currency is worth in relation to United States dollars (USD). The worth of a currency in dollars is called the exchange rate. Sometimes the exchange rate is based on the value of $100$ USD, and other times it’s based on the value of $1$ USD. To find the value of the currency in US dollars you’ll need some formulas. Here are two such formulas.

Formula

### ExchangeRateBasedon100UnitsofForeignCurrency

Example 1

You’re going on a skiing trip to Canada and brought $342$ CAD (Canadian dollars) with you. The exchange rate is $79$ USD = $100$ CAD. How many American dollars have you brought?

 $\frac{342\cdot 79\phantom{\rule{0.17em}{0ex}}\text{USD}}{100}=\text{}270$ Formula

### ExchangeRateBasedon1UnitofForeignCurrency

Example 2

You’re going on a weekend trip to London, and have brought $500$ GBP (pounds sterling, or Great Britain pounds) with you. You wonder how many US dollars that is when the exchange rate is $1\phantom{\rule{0.17em}{0ex}}\text{GBP}=1.40\phantom{\rule{0.17em}{0ex}}\text{USD}$.

 $500\cdot 1.40\phantom{\rule{0.17em}{0ex}}\text{USD}=700\phantom{\rule{0.17em}{0ex}}\text{USD}$

You have brought \$$700$ to London.

But what if you want to know how much the American dollars in your pocket are worth in a foreign currency? The formulas above can also be seen as equations. If you want to exchange the other way around, you put the known values into the equation and solve for the variable you’re looking for. See the example below.

Example 3

Iron Man and Pepper Potts are going on vacation to Norway. They’re bringing some cash and wish to exchange it for Norwegian kroner (NOK). How many NOK do they get if they exchange \$$174$, when the exchange rate is $1\phantom{\rule{0.17em}{0ex}}\text{NOK}=0.12\phantom{\rule{0.17em}{0ex}}\text{USD}$? $\begin{array}{llll}\hfill 0.12\cdot x& =174\phantom{\rule{2em}{0ex}}|:0.12\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{\text{0.12}\cdot x}{\text{0.12}}& =\frac{174}{0.12}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill x& \approx 1450\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Iron Man and Pepper will get $1450$ NOK when they exchange their money.