1972 AHSME Problems/Problem 9


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

$\textbf{(A) } 150 \qquad \textbf{(B) } 125 \qquad \textbf{(C) } 120 \qquad \textbf{(D) } 100 \qquad     \textbf{(E) } 80 \qquad$


Let $S$ be the number of sheets of paper and $E$ be the number of envelopes. We can write two equations: \[S - E = 50\] \[E - S/3 = 50\]

Solving yields $(E, S) = (100, 150).$

The answer is $\textbf{(A)}.$

-edited by coolmath34