Question

一家商店先把一件衬衫的原价提高某个百分比，再把新价格降低同样的百分比。已知最后价格是原价的 $84\%$ ，价格提高和降低的百分比是多少？

A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent. Given that the resulting price was $84\%$ of the original price, by what percent was the price increased and decreased?

$16$

$20$

$28$

$36$

$40$

答案：E

知识点：百分数平方差

难度评级：1240

视频讲解：

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文字解答：

设这个百分比写成小数为 $x$ 。涨价会把原价乘以 $1 + x$ 。

之后降价会把新价格乘以 $1 - x$ 。因此最终价格是原价乘以 $(1 + x)(1 - x) = 1 - x^2 = .84.$

于是 $x^2 = .16 \Rightarrow x = .4.$

所以这个百分比是 $40\%$ 。

正确答案是 E。

Let $x$ be the percent converted to a real number. Then the percent increase would multiply the original by $1 + x.$

The percent decrease would multiply the new price by $1 - x.$ The final price will then be the original price multiplied by $(1 + x)(1 - x) = 1 - x^2 = .84.$

This tells us that $x^2 = .16 \Rightarrow x = .4.$

This tells us that the percent would be $40\%.$

Thus, the correct answer is E.

2019 AMC 8 第 22 题

答案：E

难度评级：1240

视频讲解：

文字解答：

其他年份的第 22 题