1972 AMC 12 第 9 题

Question

Ann 和 Sue 买了相同的文具盒。Ann 每封信用

1

张纸，Sue 每封信用

3

张纸。Ann 用完所有信封后还剩

50

张纸；Sue 用完所有纸后还剩

50

个信封。每盒中的纸张数为：

Ann and Sue bought identical boxes of stationery. Ann used hers to write

1

-sheet letters and Sue used hers to write

3

-sheet letters. Ann used all the envelopes and had

50

sheets of paper left, while Sue used all of the sheets of paper and had

50

envelopes left. The number of sheets of paper in each box was:

150

125

120

100

80

设每盒有

S

张纸和

E

个信封

Let

S

and

E

be the numbers of sheets and envelopes in a box

由 Ann 的情形得

S-E=50

，由 Sue 的情形得

E-\frac{S}{3}=50

Ann gives

S-E=50

, while Sue gives

E-\frac{S}{3}=50

设每盒有

S

张纸和

E

个信封。两人的使用情况给出

S-E=50

和

E-\frac S3=50

。两式相加得

\frac{2S}{3}=100

，所以

S=150

。

因此，正确答案是 A。

Let

S

and

E

denote sheets and envelopes per box. The two accounts give

S-E=50

and

E-\frac S3=50.

Adding yields

\frac{2S}{3}=100,

so

S=150.

Therefore, the correct answer is A.

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