Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the missing $1?
We have to be careful what we are adding together. Originally, they paid $30, they each received back $1, thus they now have only paid $27. Of this $27, $25 went to the manager for the room and $2 went to the bellboy.