A trout's tail weighs eight pounds.

Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined.

What does the whole trout weigh?

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. QED.