Question #27005
posted on 01/14/2003 midnight

Q:

Dear 100 Hour Board,

Three friends go to a hotel. They are charged $30 for the night, so each person pays $10. The front desk guy realizes that he charged them $5 too much, so he gives the bellhop $5 and tells him to return it to them. The bellhop takes the money to their room. He gives a dollar to each of them, and keeps $2 for the tip. So now, each of the three guests payed $9 for the room instead of $10. However, when you multiply $9 by 3 guests, you get a total of $27. The bellhop has two more dollars, so the total amount of money involved is $29. What happened to the 30th dollar? Perhaps the answer is obvious to the all-knowing board, but please help, I've been thinking about this for too long. Thanks,

--Mook

A:

Dear Mook,

This classic problem has been used to torment many a person who does not know how to keep track of what. $25 are in the hotel cash register, $3 have been returned to the guests, and $2 are in the bellhop's hands. $25 + $3 + $2 = $30, and all the money is accounted for. The problem comes from the mindset people have when looking at this problem. They forget that the guests were ultimately not charged $30, but $25. If the guests have paid $27, that means they have overpaid by $2, not underpaid by $3. Would it have helped to think of it as just one guy and not three? Either way, I hope this helps.

--Der Berliner

Dear Mook,

This classic problem has been used to torment many a person who does not know how to keep track of what. $25 are in the hotel cash register, $3 have been returned to the guests, and $2 are in the bellhop's hands. $25 + $3 + $2 = $30, and all the money is accounted for. The problem comes from the mindset people have when looking at this problem. They forget that the guests were ultimately not charged $30, but $25. If the guests have paid $27, that means they have overpaid by $2, not underpaid by $3. Would it have helped to think of it as just one guy and not three? Either way, I hope this helps.

--Der Berliner