2002 AMC 10A 第 6 题

Question

老师要求 Cindy 从某个数中减去

3

，再将结果除以

9

。但她却先减去

9

，再将结果除以

3

，得到答案

43

。如果她按正确步骤计算，答案应是多少？

Cindy was asked by her teacher to subtract

3

from a certain number and then divide the result by

9.

Instead, she subtracted

9

and then divided the result by

3,

giving an answer of

43.

What would her answer have been had she worked the problem correctly?

15

34

43

51

138

先从 Cindy 的错误步骤还原原数。

Recover the original number from Cindy’s incorrect steps

解方程

\dfrac{x-9}{3}=43

。

Solve

\dfrac{x-9}{3}=43

设原数为

x

。由

\dfrac{x-9}{3}=43

，得

x-9=129

，所以

x=138

。

正确计算为

\dfrac{138-3}{9}=\dfrac{135}{9}=15

。

所以正确答案是 A。

Let

x

be the number. Cindy computed

\dfrac{x-9}{3}=43,

so

x-9=129

and

x=138.

The correct computation is

\dfrac{138-3}{9}=\dfrac{135}{9}=15.

Thus, the correct answer is A.

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