2009 AMC 10B 第 8 题

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

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

四月必须消去一个

1.2

的因子。

April must divide out a factor of

1.2

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.

其他年份的第 8 题