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Up Topic Public Area / Off-Topic / extra dollar?
- - By Muskrat Date 2014-08-29 10:55
3 friends are in town for a convention and decide to share the expense of a hotel room.

The clerk informs them that it will cost $30 for the night.
Each takes out $10 and pays the clerk.

When the hotel manager arrives he notes a discrepancy on the books, the room only costs $25 per night, the clerk has overcharged them.

He gives the clerk $5 and tells him to go and pay them back.

The clerk doesn't know how he's going to split $5 evenly 3-ways so he gets a bright idea.

He tells the guests that there has been a mistake and they were overcharged. He returns each $1 and decides to pocket $2.

Each gave $10 and got $1 in return so each paid $9 for the room.

Question:
Since each paid $9 ($9 x 3 = $27) and the clerk kept $2 ($27 + $2 = $29), where is the extra dollar?
Parent - By Bladerus Mortus (Councilor / Trident Captain) Date 2014-08-29 18:14
Heh funny story.

My theory: 27$ (3x9 from the guys)+3$ (3x1 back from manager)=30$
2$=clerk, so immediately 1 missing $ become 2$ in the pocket of the clerk. Let's continue this and soon we'll have a million dollars in hand :lol:
Parent - - By dr. eggman Date 2014-08-29 20:39
I also enjoyed this, thanks musk!  Took my first look before my coffee and it got me :)

Its a play on works problem that makes wrong math look right.
Lets zero it:
What people paid
27(friends) -2(clerk ) -25(hotel)=0
or 27-2-25=0
The clerk and hotel pay negative amounts as they have gained instead of lost.

We could also look at it as how much was gained
-27(friends)+2(clerk)+25(hotel)=0
or 25+2-27=0

What this puzzle does is combine these two into a math problem that looks right but really doesn't relate to the actual story.
Parent - By Muskrat Date 2014-08-29 22:48
Doc, you're a genius! :lol:
Parent - - By Patterner (Foo McQuux) Date 2014-08-30 10:02
you have to subtract the $2 the clerk kept :)

of the $30 the friends got $3 back, the clerk has $2 and the hotel the remaining $25.
Parent - By Lisa201 (Trident Captain) Date 2014-08-31 13:56
Many math classes use this example to show the distributive properties of mathematics.

3 x 10 != 3 x 9 + 2
Up Topic Public Area / Off-Topic / extra dollar?

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