AMC8 2019

AMC8 2019 · Q22

AMC8 2019 · Q22. It mainly tests Linear equations, Percent.

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

一家商店将一件衬衫的原价提高了一定百分比，然后将新价格降低了相同的百分比。已知最终价格是原价的 $84\%$ ，价格提高了和降低了多少百分比？

(A) 16 16

(B) 20 20

(D) 36 36

(E) 40 40

Answer

Correct choice: (E)

正确答案：（E）

Solution

Suppose the fraction of discount is $x$. That means $(1-x)(1+x)=0.84$; so, $1-x^{2}=0.84$, and $(x^{2})=0.16$, procuring $x=0.4$. Therefore, the price was increased and decreased by $40$%, or $\boxed{\textbf{(E)}\ 40}$.

假设折扣的分数为 $x$。那意味着 $(1-x)(1+x)=0.84$；所以，$1-x^{2}=0.84$，并且 $x^{2}=0.16$，得到 $x=0.4$。因此，价格提高了和降低了 $40\%$，或 $\boxed{\textbf{(E)}\ 40}$。

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