2023 AMC 10B 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;

a

7.5\%

tax multiplies by

1.075

Set the final cost

0.8 \times 1.075 \times P

equal to

43

and solve for

P

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.

Problem 2 in other years