We were given this problem in 8th grade algebra class. Fortunately, it was not a required assignment. Anyway, I hung on to the photocopy all these years because I think it's a fun and silly problem. See if you can figure out how to solve it. If you get really stuck or want to see if your answer is correct, contact me. Please DON'T put the answer in the public comment form along the righthand side of this page or you'll give away the answer!

A rope over the top of a fence has the same length on each side and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkey's mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkey's mother is one-half as old as the monkey will be when it is three times as old as its mother was when she was one-half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one-third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one-fourth as old as it is now. How long is the banana?

Problem from Scott, Foresman Algebra (1984)