2023 AMC 12B Problem 2

Attempt Problem 2 of the 2023 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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 work backwards

Difficulty rating: 1020

Small Hint:

A $20\%$ discount multiplies the price by $0.8,$ then the $7.5\%$ tax multiplies by $1.075$

Big Hint:

Solve $0.8\times 1.075\times p\le 43$ for the largest original price $p$

Solution:

The final cost of a pair with original price $p$ is $0.8\times 1.075\times p=0.86p.$ Setting $0.86p\le 43$ gives $p\le 50,$ so the most expensive affordable pair originally cost $50$ dollars.

Thus, the correct answer is B.

Problem 1#1

Full Exam

Problem 3#3

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