Question

Carlos 去体育用品店买跑鞋。跑鞋正在促销，每双价格降低 $20\%$ 。Carlos 还知道，他必须按折后价支付 $7.5\%$ 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：百分数不等式

难度评级：990

小提示：

$20\%$ 折扣把价格乘以 $0.8$ ； $7.5\%$ 税把价格乘以 $1.075$ 。

A $20\%$ discount multiplies the price by $0.8;$ a $7.5\%$ tax multiplies by $1.075$

大提示：

令最终花费 $0.8 \times 1.075 \times P$ 等于 $43$ ，再解 $P$ 。

Set the final cost $0.8 \times 1.075 \times P$ equal to $43$ and solve for $P$

解答：

设原价为 $P$ 。折扣和税后，Carlos 需要支付 $0.8P \times 1.075 = 0.86P$ 。他能负担当且仅当 $0.86P \le 43$ ，所以 $P \le 50$ 。因此最贵的原价为 $\$50$ 。所以正确答案是 B。

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.

2023 AMC 10B 第 2 题

答案：B

难度评级：990

小提示：

大提示：

解答：

其他年份的第 2 题