1972 AHSME Problems/Problem 9

Problem

Ann and Sue bought identical boxes of stationery. Ann used hers to write -sheet letters and Sue used hers to write -sheet letters. Ann used all the envelopes and had sheets of paper left, while Sue used all of the sheets of paper and had envelopes left. The number of sheets of paper in each box was

Solution

Let be the number of sheets of paper and be the number of envelopes. We can write two equations:

Solving yields

The answer is

-edited by coolmath34