Values of Q and T

If B + P + F = 24, what are the values of Q and T?
Hint: Consider whole numbers only.

Answer:

Since A + B = Z and Z + P = T, it follows that A + B + P = T. We also know that T + A = F, so adding the last two equations and simplifying, we get 2A + B + P = F. We know that B + P + F = 24, so we have:

24 - B - P = F
2A + B + P = F

Hence:

24 + 2A = 2F  or  12 + A = F

We can replace F with T + A. The equation then becomes 12 + A = T + A> so T = 12 and therefore Q = 19.