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The Hotel Tipping Mathematics

There were three company salesmen on a trip to find a buyer. Out of town, they needed a room for the night.

 At a local hotel, they approached the night desk manager and inquired as to the price of a room they might rent. He responded, "I have a nice room that would accommodate all three of you for $30."

 The three agreed that this is a fair rate and each chipped in $10 for the room.  They then headed upstairs.

 A few minutes later, the desk manager realized that he has forgotten this room was on "special" tonight. It should have been rented for $25. He had overcharged the threesome by $5. As an honest man (knowing that he may very well face the owner's wrath in the morning), he decided to set matters right with the salesmen.

 The desk manager sent the bellman up to their room with $5 and instructed him to refund said amount to the salesmen. The bellman knocked on the salesmen's door and, upon answering, explained the situation to the gentlemen.

 The salesmen had each contributed equally ($10) to the initial cost of the room, but there was no way that they could divide the $5 rebate equally among the three. They decided that from the $5 rebate, they would each keep $1 and that they would tip the bellman $2. All agreed that this was a fair plan and the bellman departed with his graciously accepted gratuity.

 Each of the salesmen had recovered $1 from their initial payment of $10. This means that they had each contributed $9 to the cost of the stay.

 So if they had each contributed $9 to the night, this means that:


         $9 x 3 = $27

                  + $ 2  to the bellman


where is the extra dollar?

That is a good question, but an old one.  My father said he heard this when he was like 4.  But here is your answer.  Your counting the wrong way, you subtract the $2 from the $27 leaving you $25, the cost of the room or $8.33 each.  Here is a play by play, start with the (30 - 5 = 25), (25/3 = $8.3333) or the cost of the room, then they each gave the bell boy $.66667 for a tip, which brings us to $9 flat, then each got a dollar back, bringing us to our original amount of $30 dollars ( 9 * 3 = 27 + 3 rebate = 30).  God, math questions suck, but at least they are answerable. 


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