This makes my head hurt.

[zDom]

Excerpt from an article on www.tkdtutor.com:

"A master tells how he and two male students went to a tournament and shared a room at a hotel. The clerk gave them a room for $30, so each man paid $10. Later the clerk realized the price of the room should have been $25, so she gave the bellhop five-$1 bills to return to the men. The bellhop wondered how to divide $5 between three men. Since the men did not know the real cost of the room was $25, the bellhop told them the room cost was $27, gave each of them a $1 refund, and kept the other $2 for himself.

If each of the men gave the clerk $10, that is a total of $30. If the bellhop gave each man a $1 refund, that means each man paid $9 for the room for a total of $27. Now lets to the math! The men originally paid $30. They got a refund, so now they only paid $27. The bellhop kept $2. That makes $29. What happened to the other dollar?"

Please walk me through this so I can sleep tonight

 

[Carol]

Excerpt from an article on www.tkdtutor.com:

"A master tells how he and two male students went to a tournament and shared a room at a hotel. The clerk gave them a room for $30, so each man paid $10. Later the clerk realized the price of the room should have been $25, so she gave the bellhop five-$1 bills to return to the men. The bellhop wondered how to divide $5 between three men. Since the men did not know the real cost of the room was $25, the bellhop told them the room cost was $27, gave each of them a $1 refund, and kept the other $2 for himself.

OK, got it.

If each of the men gave the clerk $10, that is a total of $30. If the bellhop gave each man a $1 refund, that means each man paid $9 for the room for a total of $27.

Correct.

Now lets to the math! The men originally paid $30. They got a refund, so now they only paid $27. The bellhop kept $2. That makes $29. What happened to the other dollar?"

Please walk me through this so I can sleep tonight

The fallacy is in trying to see meanings in the sums of two different balances (which is what you are doing by adding 27 and 2).

 

[Carol]

In case that isn't clear....look at it this way.

Three men check in to a hotel and thought it was $30 for a room, but they misheard. It was not $30 for the room, it was $13 for the room.

The clerk gives the bellhop 17 dollar bills to return to the two men.

As the bellhop cannot divide 17 dollar bills among 3 men, he pockets $2.00 and tells the men the room was $15.

So, the men paid $15 for the room, and the bellhop kept $2. Yet, the men paid $30. Summing the balances of unrelated transactions is irrelevant, as they are two unrelated mathmatical equations.



Hope that helps?

 

[zDom]

:erg:

I...um.. still don't get it.


Master, Bob, Jim each put in $10, = $30

REAL bill is $25, so $5 change, in $1s

Master, Bob, Jim each get one back, so

5-3 = 2 (for the bellhop)
and
10-1=9
10-1=9
10-1=9

27+2=29...not 30..... :headexplode:

 

[zDom]

Wait.. I think I understand now.

They don't each HAVE $9, nor have they really only paid $9.


They each HAVE $1 from the original transaction.
They each contributed to the $2 the bellhop got (so, each kicked in $9 + ($2 divided by 3)

So of the original 30,

25 goes to hotel owner
3 goes back to customers
2 goes to bellhop

and me? I finally get to sleep knowing there isn't a hole in the universe.

:whew:

 

[Carol]

Wait.. I think I understand now.

They don't each HAVE $9, nor have they really only paid $9.


They each HAVE $1 from the original transaction.
They each contributed to the $2 the bellhop got (so, each kicked in $9 + ($2 divided by 3)

So of the original 30,

25 goes to hotel owner
3 goes back to customers
2 goes to bellhop

and me? I finally get to sleep knowing there isn't a hole in the universe.

:whew:

Yep! No hole in the universe

 

[zDom]

Wait.. I think I understand now.

They don't each HAVE $9, nor have they really only paid $9.


They each HAVE $1 from the original transaction.
They each contributed to the $2 the bellhop got (so, each kicked in $9 + ($2 divided by 3)

So of the original 30,

25 goes to hotel owner
3 goes back to customers
2 goes to bellhop

and me? I finally get to sleep knowing there isn't a hole in the universe.

:whew:

Whoops -- each contributed a total of $9, part of which went toward the $25, the other part which went toward the $2 the bellhop got.

Still no hole in the universe.

(and thanks, Carol)