Puzzle Details

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?

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.

My Favourite Illusions

 Shadow Illusion Are squares A and B the same colour? Spinning Dancer Which way is the dancer spinning? Impossible Waterfall? Is the water flowing uphill in this impossible waterfall? The Butterfly A colourful butterfly?
 Duck Or Rabbit? Is this a duck or a rabbit? Hidden Faces Can you find his three daughters as well? Blind Spot An amazing demonstration of your blind spot. Impossible Prongs? Impossible prongs?
 What Am I? Can you tell what this is a picture of? Who Turned To? Who is missing? Same Colour Eyes? Are the eyes the same colour? Parallel Cafe Wall Lines? Are the horizontal lines parallel?