1972 AMC 12 第 2 题

Question

若一名经销商能把进货成本降低

8\%

，同时保持售价不变，那么按成本计算的利润率会从目前的

x\%

提高到

(x+10)\%

。则目前的利润率是：

If a dealer could get his goods for

8\%

less while keeping his selling price fixed, his profit, based on cost, would be increased to

(x+10)\%

from his present profit of

x\%,

which is:

12\%

15\%

30\%

50\%

75\%

设目前的成本为

C

，用两种方式表示同一个售价

Let the present cost be

C

and express the same selling price in two ways

降低后的成本为

0.92C

，相应利润率为

(x+10)\%

The reduced cost is

0.92C

and its profit rate is

(x+10)\%

由售价保持不变可得

\begin{aligned} 1+0.01x&=0.92\\ &\quad+0.0092(x+10) \end{aligned}\text{。}

化简得

1+0.01x=1.012+0.0092x\text{，}

所以

0.0008x=0.012

，且

x=15

。

因此，正确答案是 B。

The fixed selling price gives

\begin{aligned} 1+0.01x&=0.92\\ &\quad+0.0092(x+10). \end{aligned}

Simplifying yields

1+0.01x=1.012+0.0092x,

so

0.0008x=0.012

and

x=15.

Therefore, the correct answer is B.

其他年份的第 2 题