Answer: 64 pounds.
The head weighs 24 pounds, the body weighs 32 pounds and the tail weighs 8 pounds.
The trout is made up of the head, body and tail, H, B and T.
We are told that:
T = 8
H = T + B ÷ 2 (1)
B = H + T (2)
Placing T into (1) and (2) we get:
H = 8 + B ÷ 2 (3)
B = H + 8 (4)
Using (4) in (3) we get:
H = 8 + B ÷ 2
H = 8 + (H + 8) ÷ 2 (5)
Multiplying (5) by 2 we get:
2H = 16 + H + 8
2H = 24 + H
H = 24
Therefore, by (2):
B = H + T
B = 24 + 8
B = 32
Giving:
H = 24
B = 32
T = 8
And a total of 24 + 32 + 8 = 64 pounds.