What happen to the dollar?

[uruk]

Here is a problem that was brought to me by a student.
I'm not a math teacher so I not seeing the answer.

this may be a variation on an old trick, so stop me if you heard of this one.


Three men rent a room for 30 dollars. each man pays 10 dollars.
later, the manager tells a bellhop to give the men 5 dollars that he had overcharged them. the bell hop gives each man 1 dollar and keeps 2 dollars for himself. therefore each man has payed 9 dollars. 3 times 9 is 27 dollars plus the 2 dollars the bellhop kept.
That 29 dollars. what happened to the missing dollar? There is only 25 dollars in the till.

Whats the trick?

 

[roger]

Change the overcharge to something outrageous and run through it again. Something like "3 men rent a room for 30 million dollars...."

And you end up with the absurd question "3 times 9 is 27 dollars plus the 2 dollars the bellhop kept. That 29 dollars. What happened to the other 29,999, 971 dollars???"

In other words, there is no reason for the amount the men finally paid, plus the tip they gave to the bellop, to equal how much they were originally overcharged.

 

[epepke]

Here is a problem that was brought to me by a student.
I'm not a math teacher so I not seeing the answer.

this may be a variation on an old trick, so stop me if you heard of this one.


Three men rent a room for 30 dollars. each man pays 10 dollars.
later, the manager tells a bellhop to give the men 5 dollars that he had overcharged them. the bell hop gives each man 1 dollar and keeps 2 dollars for himself. therefore each man has payed 9 dollars. 3 times 9 is 27 dollars plus the 2 dollars the bellhop kept.
That 29 dollars. what happened to the missing dollar? There is only 25 dollars in the till.

Whats the trick?

Shouldn't this be in puzzles?

It's 27 dollars minus the 2 dollars the bellhop kept, which is 25 dollars, the amount the room actually cost.

 

[uruk]

Shouldn't this be in puzzles?

Sorry. if a moderator wants to move it , please do so
or delete it. it not important.

 

[T'ai Chi]

Three men rent a room for 30 dollars. each man pays 10 dollars.
later, the manager tells a bellhop to give the men 5 dollars that he had overcharged them. the bell hop gives each man 1 dollar and keeps 2 dollars for himself. therefore each man has payed 9 dollars. 3 times 9 is 27 dollars plus the 2 dollars the bellhop kept.
That 29 dollars. what happened to the missing dollar? There is only 25 dollars in the till.

Whats the trick?

There is no missing dollar.

At first:
man1: 10
man2: 10
man3: 10
Till: 30

Now the men and bellhop get part of that 5:
man1: +1
man2: +1
man3: +1
Till: 25
Bellhop: +2

The till amount plus the split up 5 equal the original 30.

 

[Michael Redman]

It is a classic, and well phrased to create the confusion.

 

[uruk]

There is no missing dollar.

I know but if you look at it from the renter's point of view, it goes screwy

" If I got a dollar back, that means I paid only 9 dollars for my room." the other two guys also paid 9 dollars; 3 times 9 is 27, plus the two dollars the bellhop kept; 27 plus two is 29."

It's purposefully confusing.

 

[Beerina]

It took me awhile to figure this one out when I first heard it years ago. 2 is the difference between 27 and 25, not the apparently impossible difference between 27 and 30.