1972 AMC 12 Problem 9

Attempt Problem 9 of the 1972 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1972 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

Let

S

and

E

be the numbers of sheets and envelopes in a box

Ann gives

S-E=50

, while Sue gives

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

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,

S=150.

Therefore, the correct answer is A.

Problem 9 in other years