Question

某一年，汽油价格在一月上涨 $20\%$ ，二月下降 $20\%$ ，三月上涨 $25\%$ ，四月下降 $x\%$ 。四月底的汽油价格与一月初相同。四舍五入到最接近的整数， $x$ 是多少？

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 $x?$

$12$

$17$

$20$

$25$

$35$

答案：B

知识点：百分数代数变形

难度评级：1170

小提示：

三月底价格是起始价格的 $(1.2)(0.8)(1.25)$ 倍。

After March the price is $(1.2)(0.8)(1.25)$ times the starting price

大提示：

四月必须消去一个 $1.2$ 的因子。

April must divide out a factor of $1.2$

解答：

设起始价格为 $p$ 。三月底的价格为 $(1.2)(0.8)(1.25)p=1.2p\text{。}$ 四月降价后要回到 $p$ ，所以要减少 $0.2p$ ，占当时价格的百分比为 $x=100\cdot\dfrac{0.2p}{1.2p}=\dfrac{100}{6}\approx16.7\text{。}$

四舍五入后， $x=17$ 。

所以正确答案是 B。

Let $p$ be the starting price. After March the price is $(1.2)(0.8)(1.25)p=1.2p.$ The April drop must return it to $p,$ so it removes $0.2p,$ a fraction $x=100\cdot\dfrac{0.2p}{1.2p}=\dfrac{100}{6}\approx16.7.$

To the nearest integer, $x=17.$

Thus, the correct answer is B.

2009 AMC 10B 第 8 题

答案：B

难度评级：1170

小提示：

大提示：

解答：

其他年份的第 8 题