POTW116 Solution

Answer to POTW116 is 45 kg.

Let F be the amount of free luggage allowance per person. Assuming that excess luggage are charged at a fixed amount per kilogram, the two men brought on board 2F plus $36 worth of extra luggage. On the other hand, we are told that if all the luggage belonged to one man, he would have been charged $72, i.e. he brought on board F plus $72 worth of extra luggage. So the free allowance F is equivalent to $36 worth of extra luggage. Thus 3F equals 135 kilograms and F equals 45 kg.