Problem:
Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by on every pair of shoes. Carlos also knew that he had to pay a sales tax on the discounted price. He had . What is the original (before discount) price of the most expensive shoes he could afford to buy?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let represent the original price of the shoes in dollars. The discounted price is , and is the total amount Carlos has to pay. Therefore must be less than or equal to 43 , so
The original price of the most expensive shoes he could afford to buy is .
The problems on this page are the property of the MAA's American Mathematics Competitions