Question

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?

$\$46$

$\$50$

$\$48$

$\$47$

$\$49$

Answer: B

Concepts:percentage inequality

Difficulty rating: 990

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.

2023 AMC 10B Problem 2

Answer: B

Difficulty rating: 990

Solution:

Problem 2 in Other Years