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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.

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