2500.12 – Stationery

Shawn and Rhonda bought identical boxes of stationery to write letters to their state representatives. Shawn used theirs to write 1-sheet letters, and Rhonda used hers to write 3-sheet letters. Shawn used all the envelopes and had 50 sheets of paper left, while Rhonda used all of the sheets of paper and had 50 envelopes left. The number of sheets of paper in each box was:

  1. 150
  2. 125
  3. 120
  4. 100
  5. 80
Solution

Let each box contain p sheets of paper and e envelopes. Shawn wrote p letters, so from Shawn we learn that p=e+50p = e +50. Now, Rhonda wrote p/3 letters, so from Rhonda we learn that p/3+50=e.p/3 + 50 = e.

Proceeding,

e=p–50e=p/3+50p/3+50=p−50p+150=3p–1502p=300 \begin{aligned} e &=& p – 50 \\ e &=& p/3 + 50 \\ p/3 + 50 &=& p - 50 \\ p + 150 &=& 3p – 150 \\ 2p &=& 300 \end{aligned}

So, p=150p = 150 and e=100.e = 100.

Check:

Shawn: 100 envelopes and 100 sheets of paper leaves 50 sheets.

Rhonda: 50 letters = 150 sheets of paper and 50 envelopes leaves 50 envelopes.

P.S. Do you know the easy way to remember how stationery is spelled (as opposed to stationary)? StationERy is papER.