What is the total length of the fish?

Question

A fish had a tail as long as its head pluz a quater the length of its body. Its body was three quarters of its total length. Its head was 4 in. long. What was the total length of the fish?

Answer 1

128 inches - assuming your slightly ambiguous problem means that the tail is the head length plus 1/4 of the body length. With the body being 3/4 of the overall length ? Because the head and tail only represent 1/4 of overall length and we already know that this gives 8in plus a much larger amount (remember the tail is 4in + 1/4 body length) I started with a body length of 45in. I then calculated what the other lengths SHOULD be and compared this to what I ACTUALLY got. I increased the body length by 3in each time because 3 is a common multiple and divider for thirds and quarters as is used here. I soon noticed that the gap between what result I SHOULD have got and the result I was ACTUALLY getting was decreasing by 0.25 each time I added 3in to the body length, so it was just a case of calculating how many multiples of 0.25 were needed to make the SHOULD get and ACTUALLY get results the same. This multiple was multiplied by 3 and added to the body length I was investigating at that point. Thus the answer was revealed ! Finally here is the breakdown.

Head 4in Body 96in Tail 28in. So if body is 96, tail is 1/4 of this plus 4 (24+4) 28. plus the 4 for the head = 128in. Of course the other way to check it is that the body is 3/4 total length. So 96 / 3 * 4 = 128in. What a strange looking fish indeed !!! I am sure there is a more mathematical way to do this, perhaps algebra but I am no mathematician, hence why I did it as described above !