Answer to the Problem of the Week

for the week of January 17, 2000

Solve the following problem between Monday and Friday. Then click on the icon below to e-mail your solution along with your name, city, and state.

The Five Equation Problem
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:

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