AMC12 2009 B

AMC12 2009 B · Q7

AMC12 2009 B · Q7. It mainly tests Percent, Arithmetic misc.

In a certain year the price of gasoline rose by $20\%$ during January, fell by $20\%$ during February, rose by $25\%$ during March, and fell by $x\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x$

在某一年，汽油价格在一月上涨 $20\%$，二月下跌 $20\%$，三月上涨 $25\%$，四月下跌 $x\%$。四月底的汽油价格与一月初相同。$x$ 的最近整数是多少？

(A) 12 12

(B) 17 17

(D) 25 25

(E) 35 35

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $p$ be the price at the beginning of January. The price at the end of March was $(1.2)(0.8)(1.25)p = 1.2p.$ Because the price at the end of April was $p$, the price decreased by $0.2p$ during April, and the percent decrease was \[x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.\] So to the nearest integer $x$ is $\boxed{17}$. The answer is $\mathrm{(B)}$.

设一月初的价格为 $p$。三月底的价格为 $(1.2)(0.8)(1.25)p = 1.2p.$ 因为四月底的价格为 $p$，所以四月价格下降了 $0.2p$，其下降百分比为 \[x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.\] 所以取最近整数，$x$ 为 $\boxed{17}$。答案是 $\mathrm{(B)}$。

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