2023 AMC 12B 第 2 题

Question

Carlos 去体育用品店买跑鞋。跑鞋正在打折，每双鞋的价格都降低

20\%

。Carlos 还知道他需要按折后价支付

7.5\%

的销售税。他有

43

美元。他能买得起的最贵跑鞋的原价（折扣前价格）是多少？

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

20\%

的折扣把价格乘以

0.8

，然后

7.5\%

的税把价格乘以

1.075

。

A

20\%

discount multiplies the price by

0.8,

then the

7.5\%

tax multiplies by

1.075

解不等式

0.8\times 1.075\times p\le 43

，求最大的原价

p

。

Solve

0.8\times 1.075\times p\le 43

for the largest original price

p

原价为

p

的一双鞋最终费用是

0.8\times 1.075\times p=0.86p

。由

0.86p\le 43

得

p\le 50

，所以他能买得起的最贵跑鞋原价为

50

美元。

因此，正确答案是 B。

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.

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