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, they now have only paid £27. Of this £27, £25 went to the manager for the room and £2 went to the bellboy.