September 2011
Problem of the Month

The Pencil Problem

If Jenny sells three pencils and buys an eraser, she is up ten cents.
If instead Jenny sells five pencils and buys two erasers, she breaks even.

How much is a pencil?
How much is an eraser?

Solution to the Problem:

A pencil costs 20 cents and an eraser costs 50 cents.

Let p = cost of a pencil.
Let e = cost of an eraser.
Then 3p - e = 10
and 5p - 2e = 0.
Multiply the first equation by -2 and add to the second equation:
Multiplying by -2:     -6p + 2e = -20
Then adding to the second equation:     -p = -20.
Therefore, p = 20 and e = 50.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. John C. Funk	Ventura, California
3. Tyler Cantrell	Mountain View High School, Mountain View, Wyoming
4. Halee Salsbury	Mountain View High School, Mountain View, Wyoming
5. Erin Watson	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher