2009 AMC 12B 第 7 题

Question

某一年中，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。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

知识点：百分数

将连续的倍率

1.2

、

0.8

和

1.25

相乘。

Multiply the successive factors

1.2,

0.8,

and

1.25

三个月后价格变为起始价格的

1.2

倍，所以四月必须抵消这个倍率。

After three months the price is

1.2

times the start, so April must undo that factor

一月至三月后，价格变为原价的

1.2 \cdot 0.8 \cdot 1.25 = 1.2

倍。

要回到原价，四月必须乘以

\dfrac{1}{1.2}

，也就是下降

1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%

。四舍五入后，

x = 17

。

所以正确答案是 B。

After January through March the price is

1.2 \cdot 0.8 \cdot 1.25 = 1.2

times the original.

To return to the original, April must multiply by

\dfrac{1}{1.2},

a decrease of

1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%.

To the nearest integer,

x = 17.

Thus, the correct answer is B.

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