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?

Puzzle Copyright © Kevin Stone

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Hint

A little bit of algebra might help.

Answer

64 pounds.

The head weighs 24 pounds, the body weighs 32 pounds, and the tail weighs 8 pounds.

Reasoning

The trout is made up of the head, body and tail, H, B and T.

We are told that:

T = 8

(1) H = T + B ÷ 2

(2) B = H + T

Placing T into (1) and (2) we get:

(3) H = 8 + B ÷ 2

(4) B = H + 8

Using (4) in (3) we get:

H = 8 + B ÷ 2

(5) H = 8 + (H + 8) ÷ 2

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.