Interesting Math Story Problem

[FlyUSArmy]

Well, this forum contains quite a few of you smart, engineering types. So break out your slide rules.

The following story problem is just simple math. Not calculus, not algebra, just arithmetic. Yet can be surprisingly tricky....

To make the numbers in the story low, just pretend this took place 50 years ago or so and the prices are reasonable.

Three men are travelling together on business. They check into a hotel and get three separate rooms. The bill comes to $30. Each man pays $10 and they go to their rooms.

The desk clerk then realizes he made an error. The total should have been $25 rather than $30. So he gives the bellboy $5 and tells him to give the men their change.

The bellboy thinks to himself, wait, I can’t split this $5 evenly between the three guys, and they should have given me a tip anyway. So he keeps $2 and gives each of the three men $1 back.

The men have now paid $9 each. 3 x $9 = $27. Plus the $2 the bellboy kept. Now comes to $29. But we started out with $30.

Where is the missing $1 ?

Don’t want to spoil the fun by giving the answer now. So I’ll come back with it in a day or so if you are stumped.

 

[ACMarina]

I've seen that one before. Good question, somebody might find it out but I'm not gonna tell you. .

 

[Joe Talmadge]

Heh, very cute. I figured it out, but don't want to spoil the fun. The confusion comes in conflating what's been paid with who ends up with the cash.

 

[greenLED]

This one is similar to counting your fingers backwards:
(10, 9, 8, 7, 6) + 5 (the other hand)= 11 fingers! /ubbthreads/images/graemlins/smile.gif

:son rolls eyes:

 

[Haesslich]

Heh. I saw that one pretty much right away, though I wrote down who had what at the very end to track it. /ubbthreads/images/graemlins/grin.gif I'm not going to spoil either, though.

 

[Empath]

You could ask a math student that gets wrong answers to problems, why they're wrong, and he'd probably just say because he does the problems wrong. Such is the situation here.

The two dollars pocketed by the bellboy is already part of the $27 paid by the three customers. Adding it in again is not a part of any solution to the question. The bellboy's $2 and the clerk's $25 total the $27 paid by the customers.

If you were to try to arrive at the $30, which the riddle does, then it would be $27 plus the $3 returned to them. The bellhop's ill-gotten gains aren't part of that. The bellhop's money is part of what the hotel received, $25 to the clerk, and $2 to the bellhop.

 

[Lynx_Arc]

It is easier to see it as the three customers were suppposed to pay $25 and $3 was refunded to them making $28 and the bellboy kept $2.

 

[cobb]

Lots of math riddles, problems, stories and interesting facts out there.

 

[tvodrd]

Has anyone noticed that with 2-ply TP some times when you start a new roll, you can get the outer ply "out of phase" (for lack of a better term) with its mating ply. The outer ply can overlap the inner by over an inch. If you multiply the two diameters (which differ by only the thickness of a ply) by Pi, the overlap should only be a few thousandths, not an inch. /ubbthreads/images/graemlins/grin.gif (I considered mailing that one to Marilyn.)
(Calm down Craig. /ubbthreads/images/graemlins/grin.gif )

Larry

 

[georget98]

[ QUOTE ]
tvodrd said:
Has anyone noticed that with 2-ply TP some times when you start a new roll, you can get the outer ply "out of phase" (for lack of a better term) with its mating ply. The outer ply can overlap the inner by over an inch. If you multiply the two diameters (which differ by only the thickness of a ply) by Pi, the overlap should only be a few thousandths, not an inch. /ubbthreads/images/graemlins/grin.gif (I considered mailing that one to Marilyn.)
(Calm down Craig. /ubbthreads/images/graemlins/grin.gif )

Larry

[/ QUOTE ]
Since the sheet length is not a multiple of the roll's circumference, the sheets do not normally line up from turn to turn. When you're "out of phase" you're using plies from two different turns.

 

[tvodrd]

/ubbthreads/images/graemlins/thumbsup.gif (Ya could have let some people constipate/consternate on it for a while. /ubbthreads/images/graemlins/grin.gif )

Larry

 

[ELinick]

This answer is not my own (I googled it). I do think it is the most entertaining "answer" I found and does help demonstrate the problem with the riddle.

The following night two friends check into the same motel. Once again the clerk charges them $30, or $15 per person. After the clerk remembers the total rate is only $25 he sends the bellhop upstairs with five $1 bills to pay the two friends back. The bellhop knows he got away with larceny once so he tries it again. But this time he pockets $3 and returns $2 to the hotel guests ($1 per guest). So each of the two guests got $1 back from their original $15. Therefore each paid $14 which is a total payment of $28 for the room. Now the bellhop has $3, the guests paid $28, for a total of $31.

THERE'S THE MISSING DOLLAR!!!!

 

[cobb]

At least the last post answered the question. I still have to read those several times, as I try to answer the original question, wheres the 1 dollar.