No Jokes... Just Math Problems!

(A couple of brain teasers for you!)

Three business men were travelling from somewhere Up North to somewhere Down South and stopped at a motel somewhere In Between. The man at the front desk told them they could have a large room for thirty bucks a night. They each gave the man ten dollars (3X$10=$30). Shortly after they went to their room the man at the front desk realized that he had over charged them; the room was only twenty-five bucks. Soooooo.... he gave the busboy five one-dollar bills and told him to go give the refund to the businessmen. The busboy couldn't figure out how to divide five bucks between the three men so he pocketed two and gave each man one. This means that each man paid nine dollars (3X$9=$27) and the boy made two dollars. This adds up to twenty-nine dollars ($27+$2=$29). What happened to the other dollar?

A rope over the top of a fence has the same length on each side. It 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 ot the weight of the monkey. The banana weighs two ounces per inch. The rope is as long (in feet) as the age of the monkey (in years), and the weight of the monkey (in ounces) is the same as the age of the monkey's mother. The combined ages of the monkey and its mother are thirty years. One half the weight of the monkey, plus the weight of the banana, is one fourth as much as the weight of the weight and the weight of the rope. The monkey's mother is half as old as the monkey will be when it is three times as old as its mother was when she was 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 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?