AMC10 2009 B

AMC10 2009 B · Q8

AMC10 2009 B · Q8. It mainly tests Percent, Rounding & estimation.

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，汽油价格在一月份上涨 20%，二月份下跌 20%，三月份上涨 25%，四月份下跌 $x\%$ 。四月底的汽油价格与一月初相同。四月份下跌的百分比 $x$ 取整到最近整数是多少？

(A) 12 12

(B) 17 17

(D) 25 25

(E) 35 35

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $p$ denote 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 $$ x = 100 \cdot \frac{0.2p}{1.2p} = \frac{100}{6} \approx 16.7. $$ To the nearest integer, $x$ is 17.

答案（B）：设 $p$ 表示一月初的价格。三月底的价格为 $(1.2)(0.8)(1.25)p = 1.2p$。由于四月底的价格是 $p$，因此四月份价格下降了 $0.2p$，降幅百分比为 $$ x = 100 \cdot \frac{0.2p}{1.2p} = \frac{100}{6} \approx 16.7. $$ 四舍五入到最接近的整数，$x$ 为 17。

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