Math Club - Fun & Games

"Missing Dollar"

Question:

Three men went to a hotel and were told that there was only one room left and that it would cost $30 for the night. They paid $10 apiece and went to the room. The desk clerk, discovering that by mistake he had overcharged them by $5, asked the bellboy to return the $5. The bellboy, not being as honest as the desk clerk, reasoned that since $5 is not easy to divide three ways, he would keep $2 and return $1 to each of the three men. Each man thus actually paid only $9 apiece, or a total of $27 for the room. Add to that the $2 the bellboy kept and the total is $29.

Where did the missing dollar go?

Answer:

The men paid $27 for the hotel room, but the $2 the bellhop kept is included in that $27. The remaining $3 is in the pockets of the three men, so the $30 is allocated as follows:

                               Three men:
                                                              $ 3
                               Hotel Room:
                                                              $ 25
                               Bellhop:
                                                              $ 2
                               Total:
                                                              $ 30

-- Tom Supple
Warren College '89