Where Is the Missing Dollar in the Room Rental Puzzle?

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In summary, three recent college graduates rent a room for $30 and split the cost evenly. However, the room turns out to only be $25, so the manager gives the bellboy $5 to return to the group. The bellboy takes $2 for himself, leaving $3 to be distributed among the group. The total amount paid by the group and the bellboy adds up to $30, resolving the supposed missing dollar. This is a well-known brain teaser and not a true mathematics problem.
  • #1
mineys
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So there are three guys fresh out of college who want to save money, so they decide to rent a room. The room costs 30 dollars, so they split it 10-10-10. They pay, but it turns out the room is only $25, so the manager asks the bellboy to take $5 and to give it back. The bellboy takes a 'tip' off the top, and gives back $3. So, the paid $9 each. 9*3=27. The bellboy has $2. 9*3+2=$29. Where is the last dollar?

If you know the answer or have heard it before, a simple "oooh, i get it" will suffice. Please do not spoil it for others until they are just about ready to commit suicide.

That is all.
 
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  • #2
Highlight to read: Why have you done 9*3+2=29? 9*3=27, the total amount paid (25 for the room, 2 to the bellboy), then each person gets one dollar back each, so this sums to 30.

Note, we have a https://www.physicsforums.com/forumdisplay.php?f=33 forum.
 
  • #3
Yea I've seen this one before.
 
  • #4
Ohhh i get it...lol
 
  • #5
You probably won't catch too many people around here with that one. :D
 
  • #6
i have heard it before. its a very widely known brain teaser.
 
  • #7
I think this is more of a tautology and not a maths problem.

The original total cost of the room = $30.00.
Upon review, the total cost of the room is now = $25.00.

This leaves $5.00.

If they bell man takes $2.00, there are $3.00 remaining.

25.00+2.00 = 27 + 3 = 30.

Unless I am an idiot, I don't see the dilemma. I am going to go find the solution to this and see if there is a trick or something -- it seems to straight forward to me (I have never seen this before).

EDIT: can't seem to find this problem when I google it -- did you rewrite it?
 
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  • #8
Well, I'd never heard it before, but the "solution" is clear! Just like any other brain teaser, it's meant to catch you out and disguise the answer. However, as uart says, I don't think many mathematicians will be caught out by it!
 

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