2023 AMC 12B Problem 2

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

A

20\%

discount multiplies the price by

0.8,

then the

7.5\%

tax multiplies by

1.075

Solve

0.8\times 1.075\times p\le 43

for the largest original price

p

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 2 in other years