# 9.2.1 Finding a Word Formula

## Activity: Exchanging Currencies

Suppose you are visiting Europe, and you want to exchange some money from dollars into euros. In 2011, one agency offered an exchange rate of $1.00 to €0.74 and did not make any additional charges. [ You can look up current exchange rates and fees on the Internet, or from some newspapers, banks, or travel agencies. ]

(a) How many euros would you get for $5? How many euros would you get for $10?

### Answer

(a) For each dollar, you would get €0.74, as shown below.

So, if you exchange $5, you would get €0.74 five times. , so you would receive back €3.70.

If you exchange $10, you would get €0.74 10 times. , so you would receive back €7.40.

(b) Write down a word formula that you can use to convert dollars into euros. [ What would happen to the formula if there were also a fee per transaction? ]

### Answer

(b) To change dollars into euros, multiply the number of dollars by the exchange rate of €0.74. The word formula to represent this is:

If there were also a fee per transaction this would have to be added to the formula.

(c) Check that your formula works by using it to convert $5 into euros.

### Answer

(c) Substituting 5 for “number of dollars” gives the number of euros: . This agrees with the answer in part (a).

These two examples illustrate how a word formula can be used to summarize a mathematical process such as converting units of length or currencies. Once a formula has been derived, it can then be used in other situations, both for calculations by hand or by computer—for example, for currency transactions in a bank. You will be able to practice writing your own formulas in Sections 9.4 and 9.5.

Now let's look at using formulas.

9.2 Looking for Relationships