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?
(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? ]
(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.
(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.