January 17, 2000
Problem of the Week

Five Equations

What is the value of F in the following system of equations?

A + B = Z	(1)
Z + P = T	(2)
T + A = F	(3)
B + P + F = 30	(4)
A = 8	(5)

Solution to the Problem: F = 23

Here is the complete solution:

• Substituting equation (1) in equation (2) gives
  A + B + P = T
• Substituting equation (5) in this last equation gives
  8 + B + P = T      (6)
• Substitute equation (3) in equation (4) to get
  B + P + T + A = 30
• Substituting equation (5) in this last equation gives
  22 - B - P = T      (7)

• Adding equations (6) and (7) gives the following:
  30 = 2T
  So T = 15      (8)
• Substitute equations (5) and (8) in equation (3) gives
  F = 15 + 8 = 23

Correctly solved by:

1. Jia Ran	Rome, Italy
2. Tom Marino	Winchester, VA
3. Bob Hearn	Winchester, VA
4. Court Pifer	Winchester, VA
5. Chip Crawford	Winchester, VA
6. Richard Mocarski	Winchester, VA

Send any comments or questions to: David Pleacher