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Hotel Bill

62 replies to this topic

#1 rookie1ja

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Posted 30 March 2007 - 03:25 PM

Hotel Bill - Back to the Logic Puzzles
Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives the bellboy \$5 to return to the guests. On the way to the room the bellboy reasons that \$5 would be difficult to split among three people so he pockets \$2 and gives \$1 to each person. Now each person paid \$10 and got back \$1. So they paid \$9 each, totaling \$27. The bellboy has another \$2, adding up to \$29.
Where is the remaining dollar?

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#2 Paige's Mom

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Posted 03 May 2007 - 03:07 PM

Actually, I got a totally different answer - and please tell me if I'm wrong:

For the money exchanged: The true bill was \$25 and the bellboy gave each of the three guests a \$1 back. Now, the total exchanged is \$28. And the bellboy has \$2. That equals the \$30.

For the intangible part: You can't figure in that each guest paid exactly \$9 for the room because the room bill was \$25 which can't be divided between 3 people evenly. Each person would have paid exactly \$8.33333333333333 each.

Take the \$8 x's 3 people = \$24
Plus \$3 they were given back = \$3
.33333333333333 x's 3 people = \$1 <--- the missing dollar
and the bellboy has \$2

Total = \$30

- Hope I did this right
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#3 airesso

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Posted 09 May 2007 - 06:06 PM

This has always been one of my favorite logic puzzle due to its nature of trying to misinform you and make you run with that information. The first time I heard it I spent hours trying to figure out what was up with the 29 dollars before realizing it had nothing to do with the problem, each person paid 9 dollars because the money the bell boy took is factored into their cost.
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#4 larryhl

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Posted 06 June 2007 - 03:26 PM

great example of why math can't be done under the wrong assumptions.
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#5 coolastro1016

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Posted 20 June 2007 - 02:25 AM

each person didn't pay \$9 because the total bill is \$25. \$2 was subtacted out of the equation unlike everything else was divided and multiplied. you can't multiply and divided and add and subtract in any order you want, do to order of operations. (PEMDAS)Perentases, exponents, multiply, divide, add, subtract. so remember to Please Excuse My Dear Aunt Sally.
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#6 Numenor

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Posted 20 June 2007 - 06:05 PM

My logic:
Since three dollars were returned, you're trying to get \$27 in total rather than \$30. And since they each got a dollar back, they paid \$9 each to get \$27 (\$25 to the manager and \$2 to the bellboy).
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#7 mjkrism

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Posted 20 June 2007 - 06:39 PM

They got \$3 back. So they paid \$27, inclusive of the hotel bill(\$25) and the tip to the bellboy(\$2). So if you add \$2 to \$27, it is doing it twice.
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Posted 23 June 2007 - 01:58 AM

again proof that math calculated incorrectly is always incorrect. exception to rule: I spend more than I make! GENIUS!
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#9 ppatton004729

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Posted 26 June 2007 - 10:16 PM

The variation of this goes an older couple chk into same hotel. They get charged same \$30. The fee is \$25. Bellboy is given same \$5.00 and this time decides to keep \$3, giving them back \$1 each. Now they paid \$14 each for the room, plus the \$3 in the bellhop's pocket. It equals \$31. ****There is the other dollar*****
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#10 mdsl

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Posted 27 June 2007 - 04:10 PM

That guy must be pretty cheap not to pay for his wife's half of the room AND motivate the bellhop to tip himself.
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