Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1972 AHSME Problems/Problem 9

Revision as of 21:49, 28 January 2021 by Coolmath34 (talk | contribs) (Created page with "== Problem == Ann and Sue bought identical boxes of stationery. Ann used hers to write <math>1</math>-sheet letters and Sue used hers to write <math>3</math>-sheet letters....")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

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

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

Solution

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1972_AHSME_Problems/Problem_9&oldid=143690"