May 2010
Problem of the Month

Four By Four
by William Jacob Bechem

The sum of four numbers is 100.
If you add 4 to the first number,
subtract 4 from the second number,
multiply the third number by 4, or
divide the fourth number by 4,
the result will be the same.

What are the four original numbers?

Solution to the Problem:

The numbers are 12, 20, 4, and 64.

If your 4 numbers are called, w, x, y, and z,
you have w + 4 = x - 4 = 4y = z/4.
From this, the four numbers can be represented as
w, w + 8, (w + 4)/4, and 4 (w + 4).
Then solve for w in the equation:
w + w + 8 + (w + 4)/4 + 4 (w + 4) = 100.
w = 12.
Substitute to get the other three numbers.

Correctly solved by:

1. Tawny Bugas	Mountain View High School, Mountain View, Wyoming
2. John Funk	Ventura, Californina
3. Fawn Nguyen	Somis, California
4. Katie Hyde	John Handley High School, Winchester, Virginia
5. Brian Packham	Anderson Middle School, Anderson, California
6. David & Judy Dixon	Bennettsville, South Carolina
7. Austin Hale	Mountain View High School, Mountain View, Wyoming
8. Jeremy Harmon	Mountain View High School, Mountain View, Wyoming
9. Marci Harvey	Mountain View High School, Mountain View, Wyoming
10. Cassie Henry	Mountain View High School, Mountain View, Wyoming
11. Kaycie Rees	Mountain View High School, Mountain View, Wyoming
12. Tori Johnson	Mountain View High School, Mountain View, Wyoming
13. Brandon Preston	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher