9.2.1 Finding a Word Formula

Activity Symbol 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 Symbol

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. dollar five equals five postfix multiplication € 0.74 equals € 3.70, so you would receive back €3.70.

If you exchange $10, you would get €0.74 10 times. dollar 10 equals 10 postfix multiplication € 0.74 equals € 7.40, 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? ]

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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:

number of euros equals number of dollars prefix multiplication of 0.74

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

number of euros equals number of dollars prefix multiplication of 0.74 postfix plus transaction fee

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

Answer Symbol

Answer

(c) Substituting 5 for “number of dollars” gives the number of euros: five multiplication 0.74 equals 3.70. 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

9.3 Using Formulas