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.