A fish is made up of three parts: head, tail and body.
The tail is equal in length to the head, plus one-quarter of the length of the body.
The body is equal to three-quarters of the entire length of the fish.
The head is 4cm in length.
How long is the entire fish?
SOLUTION
Let's pose this in the following way:
T = Tail
B = Body
H = Head
L = Total Length
Therefore:
4 + 4 + 1/4 B + 3/4 L = L
Which can be simplified to give:
8 + 1/4B + 3/4L = L
Look also at the relationship between the Tail, Body and Total Length. The body, so we're told, is 3/4 of the Total Length and the fractional part of the tail is 1/4 of the length of the body. This means that we must be able to describe the fractional part of the tail in terms of the Total Length:
1/4 x 3/4 = 3/16
So the fractional part of the tail is 3/16 of the length of the fish!
Now we know that, we can work out what proportion of the fish the fractional part of the tail plus the body is:
3/16 + 3/4 = 3/16 + 12/16 = 15/16
So the fractional part of the tail and the body account for 15/16 of the Total Length, giving us:
8 + 15/16 L = L
What of the remaining 1/16 L? Well given the above, 1/16 L must be equal to 8 which means:
8 x 16 = Total Length = 128
So the fish must be 128cm in length! Lets try it:
1/16 L + 3/16 L + 12/16 L = 1/16 x 128 + 3/16 x 128 + 12/16 x 128 = 8 + 24 + 96 = 128
