Yet another math puzzle

I didn't get the math gene, so just about any kind of math teaser is a mystery to me. After many years I still can't explain this old puzzler:

Three men checked into a hotel, sharing one room. The desk clerk charged them $30, with each man contributing $10. Later, for whatever reason, the desk clerk decided he had overcharged the men, so he sent the bellhop upstairs with a $5 refund. On the way up the bellhop determined that he didn't know how to divy up $5 three ways, so he pocketed $2 and gave each man $1.

So, at this moment in time each man was out $9 on the room. Three times $9 is $27. Add the $2 kept by the bellhop and you get $29. Where's the missing $1?

And they say figures don't lie! Like you, I gave up on that one years ago. And I have seen others along the way. Can't remember any of them. Heck, I am happy if I can just keep my checkbook balanced!

Just another case of figer don"t lie but liers know how to figer.
three x nine =$27 + the $3 dollars each got back = $30 bellhop still gets his $2.
that clear it up?

Oh, yeah.....thanks a lot. (?!?)

The hotel collected $30 for the room. Each man owed one third or $10. The hotel later adjusted the price and charged them $25 for the room. Each man then owed 8 and one third dollar. The bell hop gave each man a one dollar refund. 9 and one third dollar times 3 equals $28. Add the $2 the bell man kept and you get the original $30.
It's all in how you tell it

Thee is no missing $. you are working on an incorrect figure of $30 whereas it should be $25.. the actual cost being $27.
25 the hotel, 2 the bellhop = $27 [3x9]

Actually the men were out 25 for the room and 2 dollars buyer's premium (bell boy tip).
See how I even made it TRACTOR related.
Hint buyers premium like at an auction!!!

In the original you should be subtracting the $2 kept by the bell boy instead of adding it.
30 - 3 - 2 = 25 room cost.
KAW

Oversight there, and $3 went to charity.

Another try.
The missing $ is the partial cost of the room not considered.
25 divided by 3 equals $8.3333 whereas when the dollar is returned it is taken from the 10 instead of adding it to the cost $8.3333 which would make outlay $9.3333. add what bellhop pocketed $0.6666 makes the $10.
So the missing dollar is in the fraction .3333x3 dropped.

cost $9 x3 = 27 bellhop $2 = $29 plus fraction dropped $1 = $30 [3x$10]

What Keith said.

This following statement is wrong, tho it sounds good it is totally wrong, bad math, a slight of hand with the words to make you forget math:

> So, at this moment in time each man was out $9 on the room. Three times $9 is $27. Add the $2 kept by the bellhop and you get $29. Where's the missing $1?

No.

At this moment, each man was out $9 _total on the room AND tip_, not just _on the room_. And tht is what sets up the error....

Three x 9 = $27 which is the total they spent.
MINUS the $2 tip, leaves the $25 the room cost.


The story is false, it is trying to say:

You start with 27 spent on the room (not true!) and add the $2 tip to this (why? The tip is already part of the $27?) to come up with $29 - which is a meaningless number. It looks good in English because they use words to preform a slight of hand, but is not mathamatically correct.

The words are trying to say 27 equals 27 plus 2 - and that is a false statement.

Or another way, the words are trying to say the cost of the room and tip is equal to the cost of the room and tip plus the tip - which is nonesensical to count the tip twice.

Clear as mud right?

-->Paul

$30 (original amount) - $3 (total back to men) - $2 (bellhop kept) = $25.

You subtract the $2 tip, not add it back to the $25.