PSAT Math Grid-Ins Question 145: Answer and Explanation

Question: 145

A currency conversion store at an airport in New York City posts the following conversion rate table.

Currency Type	Currency per 1 U.S. Dollar
U.S. dollar	1.00
Euro	0.90
Indian rupee	68.01
South African rand	16.17
Japanese yen	116.36
Australian dollar	1.41

The conversion store charges 1 percent of the amount converted plus a $2 flat fee for each total transaction (including multiple-currency exchanges as long as they take place in a single visit to the store). The flat fee is assessed in addition to the 1 percent conversion fee.

Andrew has come back to the United States from a trip to Asia and wishes to convert 700 Japanese yen and 900 Indian rupees. If he converts them to U.S. dollars at the airport currency store, how many U.S. dollars will he have from this conversion after the store transaction is complete to the nearest tenth of a dollar? (Ignore the dollar sign when gridding in your answer.)

Correct Answer: 17.1

Explanation:

17.1 First, recognize that the store takes 1%, or 0.01 of the amount converted, leaving 99%, or 0.99, of the amount you started with. Therefore, instead of converting 700 Japanese yen, you're converting 0.99(700) = 693 yen, and instead of converting 900 Indian rupees, you're converting 0.99(900) = 891 rupees.
Next, use the conversions to cancel out the units you don't want (yen and rupees) to leave you with the unit that you do want (USD):

Add these together to get 5.96 + 13.10 = 19.06. However, the store charges a $2 flat fee, so Andrew would end up with 19.06 - 2 = 17.06. When rounded to the nearest tenth of a dollar, we get 17.1.