Fun math problem

[Locke]

For some reason this old math problem came into my head. I had forgotten how much fun the confused look on peoples faces were. I'm sure most of you have heard this or can figure it out quite easily.

Three friends while on vacation stop into a hotel for rooms for the night.
Speaking to the manager, he tells them that there is only one room left and that all the other hotels in town were booked because of a conference.
They agree to share the room and the cost.
The manager tells them that it will be $300.
They each hand $100 over to him.
($100*3= $300)
When the bellhop returns from showing the friends to their room; the manager calls him over and says that he made a mistake and charged the travelers the weekend rates and that the room should only cost $250
The manager gives $50 dollars in $10's to the bellhop and asks him to refund the money to the travelers.
On the elevator ride up the bellhop can't figure out how to break the refund up evenly. So he decides to give each traveler $10's and to keep $20 for himself.
So now the friends have each paid $90's for their room and the bellhop kept $20
($90*3=$270 plus the $20 the bellhop has equals $290)
Where is the extra $10?

[cousinbasil]

There is no $300. 3 x $90 = $270. The room only costs $250, but the three of them have shelled out a total of $20 more than that, which the little fucker bellboy kept.

[Locke]

Exactly. That little bastard! :-)

[Anders Schlander]

For some reason this old math problem came into my head. I had forgotten how much fun the confused look on peoples faces were. I'm sure most of you have heard this or can figure it out quite easily.

Three friends while on vacation stop into a hotel for rooms for the night.
Speaking to the manager, he tells them that there is only one room left and that all the other hotels in town were booked because of a conference.
They agree to share the room and the cost.
The manager tells them that it will be $300.
They each hand $100 over to him.
($100*3= $300)
When the bellhop returns from showing the friends to their room; the manager calls him over and says that he made a mistake and charged the travelers the weekend rates and that the room should only cost $250
The manager gives $50 dollars in $10's to the bellhop and asks him to refund the money to the travelers.
On the elevator ride up the bellhop can't figure out how to break the refund up evenly. So he decides to give each traveler $10's and to keep $20 for himself.
So now the friends have each paid $90's for their room and the bellhop kept $20
($90*3=$270 plus the $20 the bellhop has equals $290)
Where is the extra $10?

$90*3=$270 plus the 30 dollars that they kept = 300 dollars. You are wrong to say 270 plus 20 since the 20 were included in the 270. We know this because all the money came from them, and 270 dollars came from them.


we know they kept 30 dollars from the bellhop, so the last sentence doesn't make sense (it would be the last 30 dollars, as those weren't counted yet) but then there would be 320 dollars....the problem being that the bellhops money have been counted twice. Take those extra 20 away, and you have 300!.... shouldn't this be in worldly matters though? :)

[Locke]

Too right :-)

Sorry about where I posted it. I'm new to the forum and have only posted on the Genius forum. Didn't even think to look around.

It's correct that the information is relayed incorrectly. It sounds correct to most people when they hear it though. I love when they start counting on their fingers to try to work it out.

[Philosophaster]

Easiest way to think of this is simply to tally the money at each step:

Manager has $300.

Manager gives bellboy $50, so now manager has $250 and bellboy has $50.

Bellboy gives customers $30 (out of the $50), so now manager has $250, customers have $30, and bellboy has $20.

250+20+30=300, so there is no missing $10. :-)

[paco]

I know the answer,,,If you multiply....haha.


Jesus

[paco]

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