AMC10 2023 B

AMC10 2023 B · Q2

AMC10 2023 B · Q2. It mainly tests Percent, Interest / growth (simple).

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?

卡洛斯去体育用品店买跑鞋。跑鞋打折，每双鞋价格降低 $20\%$ 。卡洛斯还知道他需要支付折扣价的 $7.5\%$ 销售税。他有 $\$$43 。他能买的最贵的鞋的原价（打折前）是多少？

(A) \$46 \$46

(B) \$50 \$50

(D) \$47 \$47

(E) \$49 \$49

Answer

Correct choice: (B)

正确答案：（B）

Solution

The discounted price of the shoes is 20\% off the original price. This means the customer pays \[ 1 - 0.20 = 0.80 \] (or 80\%) of the original price. There is also a 7.5\% sales tax, so the final amount paid is \[ 0.80 \times 1.075 = 0.86 \] (or 86\%) of the original price. Let $x$ be the original price. Then \[ 0.86x = 43. \] Solving for $x$, \[ x = \frac{43}{0.86} = 50. \]

鞋的折扣价是原价的20\% off。这意味着顾客支付 \[1 - 0.20 = 0.80\] （或80\%）的原价。还有7.5\%销售税，所以最终支付金额是 \[0.80 \times 1.075 = 0.86\] （或86\%）的原价。设 $x$ 为原价。那么 \[0.86x = 43。\] 解得 \[x = \frac{43}{0.86} = 50。\]

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