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?

$46$

$50$

$48$

$47$

$49$

答案：B

知识点：百分数逆推法

难度评级：1020

小提示：

$20\%$ 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 $1.075$

大提示：

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 $p$

解答：

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.

2023 AMC 12B 第 2 题

答案：B

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 2 题