A math problem...sorta - and no this ain't another math thread...sorta

[iPwn]

Three guys walk into a hotel after a long day. When they approached the clerk, they were told that there was only a single room left and the cost was $30. So, each guy pitches in $10 and heads up to the room. Now, after they leave the counter, the clerk realizes that the room was only $25 and sends for the bell boy to give them their money back.
On his way to their room, he contemplates how he's going to give three people $5. Instead of giving them the full $5, he decides to give each guy $1 and pocket the remaining $2.
Now that each party member received $1 back, they each essentially paid $9. Now if you multiply 9 by 3 you get $27, plus to the $2 that the bellhop has and that makes $29.
Where's the other dollar?

Now, I've posed this question to many a smart man, and I've heard a few solutions which I'm curious about. The most obvious answer is that it's only the way it's worded makes it seem like the math is imperfect. However, I also heard from my highschool math teacher, when asked this question, that this just proves how imperfect of a science math is. I'm not so inclined to believe that one though.

Thoughts?

 

[detox1]

a loophole, I'm sure, our governments are well aware of.

on a larger scale..

 

[superman22x]

What? No, they spent $27. The room cost $25. The other $2 went to the bellboy. You can't add the two to the $27, lol. They spent $30, got $3 back. They spent $27 overall. And $2 went to the bellboy.

 

[Lowndsey]

Of course it is the way it's worded.

 

[JogaBonito1502]

You have to look at it as a system. The wording of the problem redefines the system halfway through the problem statement, taking the hotel out of the equation and leaving just the bell boy and the 3 men. Look at this this way:

The balances are the following:
-Hotel: $0
-Bell Boy: $0
-3 Men: $30

After the pay the clerk:
-Hotel: $30
-Bell Boy: $0
-3 Men: $0

After the clerk gives the boy money:
-Hotel: $25
-Bell Boy: $5
-3 Men: $0

After the boy gives the men their dollar:
-Hotel: $25
-Bell Boy: $2
-3 Men: $3

The wording redefines the system when you don't consider the bell boy as part of the payment for the room. It is as Superman says.

edit: This is analogous to internal forces. The values of internal forces of an arbitrary body at rest or at constant speed may change depending on the conditions, but the body is not accelerating. The overall balance of the system above does not change, just the location of the money.

 

[Siriann]

They paid $30 -- it was only $25 so each man got $1 back which equals $28 dollars in total (25 + 1[3]). Plus the bellboy's $2 that equals $30.


I'm drunk, though...

 

[iPwn]

Don't get me wrong, I understand that it's a play on words, I guess Joga really puts it into perspective though.

 

[superman22x]

They paid $30 -- it was only $25 so each man got $1 back which equals $28 dollars in total (25 + 1[3]). Plus the bellboy's $2 that equals $30.


I'm drunk, though...

lmfao, on a wednesday?

Don't get me wrong, I understand that it's a play on words, I guess Joga really puts it into perspective though.

It's more just adding when you are supposed to subtract...

 

[iPwn]

Well now let's go the other way with it. Each man literally paid $9 right? 9x3 = 27, plus the $3 from the men equals thirty, now you have the two that the bellhop took coming up as surplus...

 

[Luke_Uk_Baggy]

I understand this, from both sides, after 10 mins of thinking. Hope this helps!

The problem side:

The got $1 back each, so they paid $9 each. 9 x 3 = $27. $2 for the boy, Wheres the other $1 ?!?


Solution side. Room was $25. They paid $30. They all got $1 back, so $28 was paid, and the boy had $2. = $30. No 'spare dollar'


Solution (Explained) The only other thing people will get stuck on is this;

If they all got $1 back each, then technically, they did pay $9 each, right? , and the bell boy gets $2. (The wording that catches you out is the next bit) 'So where is the other $1' This automatically assumes you are adding another dollar to make it up to $30, and you are missing it.

You need to drill it into your head that The new room price is $25. If they all get $1 back, they are paying $27 between them, for a $25 room. In this scenario, they have overpaid by $2, in total. They dont see this because the boy has taken it as a tip. They all have their change, the boy has his tip, and the $25 room has been paid for. There is no extra dollar.

The question gets you trying to find an extra dollar, but you just need to remember the room is $25, and not $30, therefore it works out.

(I THINK that makes sense!)