Where's the dollar?

[Lord of Delusions]

Three men are on a buisness trip and stop at a motel. A room costs $30, so each man pays $10 and they split one room.

Later on the night manager notices that the room they were given only costs $25, so he gives the bell boy five one dollar bills to give back to the men.

On his way to the room, the bell boy realizes he can't split the $5 three ways, so he pockets $2. When he gets to the room he gives each man $1.

************************

Since each man recieved $1 change for the $10 they originally paid for the room, they actually only paid $9 each. 3 men x $9 = $27.

The bell boy pocketed $2. $27 + $2 = $29.

Where did the $1 go that would equal the original $30 price paid for the room?



Apparently only 3% of the people that read this little problem figure it out (I wasn't one of them, I had to cheat and read the answer), and most of those that do are female, so this should be interesting!

 

[Lord of Delusions]

Nobody?

 

[spideyjg]

Nobody?

My brain cells are maxed out this week. I can't fire up enough of them to try and figure that one out. :zombie:

Jim

 

[Metallicat180]

The bell boy was on the trip and staying in the room too?? I dunno, that's a tough one!

 

[Puckfiend]

There is no missing dollar..it's how you look at the problem. The way it's worded throws you off somehow.

Manager has...$25.
Bellhop has.....$2.
Renters have..$3.

Total: $30.

 

[MattDouglas]

I'm with puckfiend on this one.

If I pay $5 for something that cost $4, and then I get $1 change, then there is nothing mysteriously missing. The supopsed extra dollar is part of the $30 that the manager was paid, but he or she gave it back to the customers as any honest person would do.

 

[Downshifter]

I agree with puck.

...and I question the morals, and ethics of 3 businessmen sharing a $25 dollar room .

 

[darthrya]

Just saw this.

It's quite confusing, but very simple if you dissect it.

There is no missing $1 because in the end, the manger got $25, the bellhop got $2, and the businessmen got $3 back. The total is $30.

The trick is in the workding of the question, which takes on a two-dimensional view, instead of a three-dimensional one (three parties). The wording takes the manager out of the equation, and it results in two-dimensional math of incorrect calculations. $30-$3+$2=$29, not $30. Where is the manager and his $5 loss in the equation? It should be $30-$5(manager's deduction)+$2(to the bellhop)+$3(to the businessmen)=$30.

:Smug:

Edit: I want to ask, where the hell can you find a motel room for $30?

 

[Lord of Delusions]

You guys got it! And yeah, that last bit of math does throw you off.

As far as a $30 dollar motel room that 3 men can share? I don't, nor would I think I would want to, know.

 

[darthrya]

Well, I don't want to share the room. I'm just looking for one for $30 since everywhere I travel, the cheap places are $40 or more.

 

[Freddy Krugerrand]

The reason this is hard for some people to get is because the question asks you to agree to facts that are just plain wrong. But, because the math is simple there is the tendency to agree with it.

The men did not pay $9 each, two of them paid $8.33 and one of them paid $8.34 which totals to $25 (spot on). The fact that they each got a dollar back is the only reason it seems they only paid $9 each.

The question goes on to reinforce the error by saying you should add the $2 that the bellboy stole when calculating the cost to each man. The $2 was not added cost, it was a portion of a refund that the bellman stole. So, $9x3=$27 MINUS the $2 is $25 (spot on again).

To make it clear, some people will need to read more. The men actually paid $27 for the room. The fact that the bellman stole two dollars does not change that. Assume that the bellman gave the whole five dollars back and they in turn gave him a $2 tip. The math would then be $30-$5=$25 (the cost of their room) PLUS $2 (the cost of the tip) = $27 paid (again, spot on). There is no missing dollar and there is no spoon.