What happened to the last dollar?

[Hydrantman]

Three coin collectors are in town for the convention and get a hotel room that cost a total of $30 for the night. Each guy thought it would be fun to pay the bill with 10 silver dollars. The manager was so taken by this that he decided to only charge $25 for the room. He gave the bellhop 5 of the silver dollars back to give back to the guys in the room. On the way up, the bellhop tries to figure out how to divide $5 for 3 people. So he decides to give each guy back $1 and keep $2 for himself.

Now then, this means that after getting a dollar back, each man only paid $9 for the room instaed of $10. So....

$9 x 3 = $27 + $2 (kept by the bellhop) = $29
They each paid $10 up front for a total of $30 for the room. Where did the last dollar go?

 

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[fyrfighter17]

you are still adding the $2 a second time $25 for the room and $2 for the tip for a total of 27..then you're saying plus 2 where is this plus 2 coming from

 

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[Immy]

May I wade into the fray...

It's all how you interpret "got back." The minute the manager gave the bellhop the $5 discount to pass along to the three men, the transaction ends there. The men have now paid $25 ÷ 3 which = $8.33 each. There is no missing dollar because the men never "got back" their entire $5, thus you can't say they paid only $9 each because they never got their entire refund. The bellhop's decision to keep some of it changes the original equation. Plus he shouldn't have been confused on how to distribute $5 among three men. He should have simply knocked on their door and given them the fiver. End of story. But nooooo, he had to pocket $2 and complicate things.

 

[Hydrantman]

you are still adding the $2 a second time $25 for the room and $2 for the tip for a total of 27..then you're saying plus 2 where is this plus 2 coming from

You're not getting it... The $25 for the room is not the issue. You are one of the guys... you orginally paid $10. The bellboy gives you back $1 meaning you ended up only paying $9. The three of you then in fact paid $27 for the room.... not $25. The bellboy keeps the extra $2 that he never gives you guys. 27+2=29

 

[fyrfighter17]

you are still adding the $2 a second time $25 for the room and $2 for the tip for a total of 27..then you're saying plus 2 where is this plus 2 coming from

You're not getting it... The $25 for the room is not the issue. You are one of the guys... you orginally paid $10. The bellboy gives you back $1 meaning you ended up only paying $9. The three of you then in fact paid $27 for the room.... not $25. The bellboy keeps the extra $2 that he never gives you guys. 27+2=29

ok so what about the 3 they did get back add that to the mysterious $29 total and u get 32 (not fighting with you,actually havin fun with this) personally I think they should get the $29 add it to the 3 and leave with a profit and go stay at red roof inn LMAO

 

[TT]

In college I was always told that in physics you only needed to know one equation and all others could be derived from it. What is the equation you ask? F=ma. Now that we are all inspired by the great equation, and doing several derivations, one comes up with the following solution. The men originally paid $30 for the room and each recived a dollar back, meaning they paid $27 total for the room. They did not know the room was $25 and they did not know the bellhop kept $2 for himself. But the magic equation tells us that $25 for the room plus $2 for the bellhop equals the $27 that three outlayed for the room. We all should bow to the magic equation, of course it only applies to Newtonian physics....if it were quantum physics, well then another magic equation and outcome would have occured.

Thought for the day: You cannot exceed the critical radius of a black hole and live to tell about it.

 

[Hydrantman]

you are still adding the $2 a second time $25 for the room and $2 for the tip for a total of 27..then you're saying plus 2 where is this plus 2 coming from

You're not getting it... The $25 for the room is not the issue. You are one of the guys... you orginally paid $10. The bellboy gives you back $1 meaning you ended up only paying $9. The three of you then in fact paid $27 for the room.... not $25. The bellboy keeps the extra $2 that he never gives you guys. 27+2=29

ok so what about the 3 they did get back add that to the mysterious $29 total and u get 32 (not fighting with you,actually havin fun with this) personally I think they should get the $29 add it to the 3 and leave with a profit and go stay at red roof inn LMAO

This is fun aint it? But you still wrong!

 

[Montana Jim]

I don't coin role hunt but will reply anyways...

The three men spent 27 dollars... period. (9+9+9=27)

The bellhop took 2 dollars from the 27 dollars... period. (25 to the hotel)

Each man got 1 dollar back... period. (1+1+1=3)

27 spent + 3 back = 30

Stop ADDING the 2 dollars to the 27 dollars... it's not the case.

 

[Immy]

Here's another angle -

You can't say the men paid $27/$9 each for the room because the manager finalized the deal at $25/$8.33 each (or more accurately, two @ $8.33 and one @ $8.34 to even it out). If the bellhop had simply given them back the whole $5 (damn greedy bellhops!) they could have come to this conclusion.

What's confusing the issue is the leftover $5. One fact is irrefutable - that $5 is [green]change[/green] and now has nothing to do with what they paid for the room. But the men don't know there's been a $5 deduction, unless the bellhop confessed he took $2. That's the unknown variable here: how did the bellhop explain a $3 refund to the guys instead of $5?

 

[ferrabi]

nice

i had a book with these type of problems before. i forgot what the technical name for it is . but when the problem is rearrenged sometimes one digit is added or deleted.

here is a similar

Embedded media from this media site is no longer available

 

[Montana Jim]

Think spacially... and STOP ADDING 2 dollars to the 27 dollars! It taken FROM the 27...

Give each dollar an assigned number to track it... You can see 30 dollars are accounted for...

Hotel Men Bellhop
1 26 29
2 27 30
3 28
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

 

[ferrabi]

nice, best explanation for it

Think spacially... and STOP ADDING 2 dollars to the 27 dollars! It taken FROM the 27...

Give each dollar an assigned number to track it... You can see 30 dollars are accounted for...

Hotel Men Bellhop
1 26 29
2 27 30
3 28
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

 

[Hydrantman]

I'm not ADDING the $2 to the $27... the $27 is what they all eventually paid PLUS the $2 that the bellhop kept for himself. Thats $29

 

[ferrabi]

i thought that they paid only 25 eventually??

 

[TT]

Hydrantman...perhaps your "lost" dollar was due to a shorted CWI roll of halves.

 

[Montana Jim]

I'm not ADDING the $2 to the $27... the $27 is what they all eventually paid PLUS the $2 that the bellhop kept for himself. Thats $29

Ahhh... but, you are. Reread that... you just added it.

It's NOT plus... the 2 came from the 27. leaving 25 for the room, 2 for the bellhop = 27.

 

[Hydrantman]

Hydrantman...perhaps your "lost" dollar was due to a shorted CWI roll of halves.

I have only had one roll short since I started this so I guess I've been lucky so far.... I was also short a dollar in a roll of Monroes but I have found 12 dimes in 3 bags of pennies so I guess I'm even. So maybe I need to go through a couple more bags of pennies and find 10 more dimes to get that extra dollar.

 

[Hydrantman]

I'm not ADDING the $2 to the $27... the $27 is what they all eventually paid PLUS the $2 that the bellhop kept for himself. Thats $29

Ahhh... but, you are. Reread that... you just added it.

It's NOT plus... the 2 came from the 27. leaving 25 for the room, 2 for the bellhop = 27.

Ok lets look at it your way.... 30 - 27 (that the guys paid) MINUS 2 (that the bellhop took) = 1 missing dollar!!!!!!!! *LMAO*

 

[Montana Jim]

I'm not ADDING the $2 to the $27... the $27 is what they all eventually paid PLUS the $2 that the bellhop kept for himself. Thats $29

Ahhh... but, you are. Reread that... you just added it.

It's NOT plus... the 2 came from the 27. leaving 25 for the room, 2 for the bellhop = 27.

Ok lets look at it your way.... 30 - 27 (that the guys paid) MINUS 2 (that the bellhop took) = 1 missing dollar!!!!!!!! *LMAO*

Yer killin me...

Where did that come from? Your just jamming numbers together without thinking... all you have to do is ACCOUNT for the total... not add what was paid to what was kept... ALL the money is OUTGOING... not added to anything.

The guys kept: 3.00
The hotel kept: 25.00
The hop kept: 2.00
Total: 30.00

did you see my assigned numbers post above?

 

[Montana Jim]

wait now that I really look at it you're counting the $2 kept by the bell boy twice they paid 25 for the room not 27 and the bell boy kept 2 for a total of 27 add the 3 returned and u get 30

This is a correct reply... he got it right.

 

[Hydrantman]

OK OK I guess I've had about as much fun with this as I can... so here is the answer and I'll write so that all CRH can understand it.

Answer to The Missing Dollar
To look at it from the standpoint of the original $30. (10 marked with green slashes, 10 marked with "24", and 10 marked with the date)
Each man has $1. (each with the added mark of the neck painted red)
The bellhop has $2. (with dot marks added to them)
The hotel clerk has $25. (that he will drill holes in later)
Total
$1 x 3 = $3
2
25
$30