2023 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by

20\%

on every pair of shoes. Carlos also knew that he had to pay a

7.5\%

sales tax on the discounted price. He had

43

dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy?

Show solution

Solution

Let

P

be the original price. After the discount and tax, Carlos pays

0.8P \times 1.075 = 0.86P.

He can afford it when

0.86P \le 43,

which means

P \le 50.

So the priciest shoes he can swing start at

\$50.

Therefore, the answer is B.