Traveling salesman hotel room riddle

This is an old one but some may not have heard it.


Three traveling salesman stop at a hotel for the night, they ask how much is a room. The manager says the room is $30. Each man puts a $10 dollar bill on the counter, they get the key and go to there room.

The manager notices that he made a mistake, the room is only $25 not $30. He gives five $1 dollar bills to his assistant to return to the gentleman. The assistant walks to the room thinking that he can't give $5 dollars to 3 people. He gets to the room and gives each man one dollar back and keeps two for himself.

Each man(3) spent $9=$27
The assistant kept $2
That's a total of $29!

What happen to the last dollar?

Room tax?

Actually, there is no "last dollar." If you're going to deal with the amount spent by the guests and the amount stolen by the assistant, you should substract the two dollars, not add it. The room costs $25, the guests spent a total of $27, and the assistant stole the $2 difference.

The manager originally took in $30, he gave $5 to the assistant, of which $3 went to the guests, and $2 went to the assistant. $30 minus $3 = $27.

Each guest spent $9, for a total of $27. The room really costs $25. The assistant stole the $2 difference. It all checks out.

Ed

so there is no catch?

That one drive me insane last because i could only come up with the figures that pointed to no last dollar..

27+2 is still only 29 though
They each paid 10 and got back a dollar. So they each paid 9. 9x3= 27
The guy stole 2. 27+2=29

This is a crack in our mathematical structure!

And if you start with $30 and subtract the$2 the bell hop stole... 30-2=28.

A mathematical equation has to add up when completed from either direction. And this one does not.

It does if you pay attention to what Ed said:

$25 room
+$3 refund
+$2 stolen
________
$30 total


Or if you want to run it the other direction:

$30 total
-$3 refunded
-$2 stolen
_________
$25 room


Your problem is that you think you're trying to get the original amount spent, when you're actually trying to get the actual cost...

There are a number of ways to look at the actual math behind this one. The reader is misled when the riddle states that the three men each paid $9 for the room. Naturally, our mind reinforces this by thinking if each man handed over a ten dollar bill and each man got $1 back, then they each paid $9. First let's consider that the room was $25. Divide that by 3 and you get $8.33. This is what each man actually paid for the room. They each received a dollar back. Add $1 to $8.33 and you get $9.33. So each person can now account for $9.33. Multiply that times 3 and you get $28. Add the $2 that the bellboy kept and you get $30, which is the original amount they started with.

Another way to figure it is like this. They each originally paid $10. The room was $25 and $3 was returned to them, so that totals $28. The bellhop kept $2, and when you add that, you are back to $30.

The men did pay $9 each for the room which does equal $27, the $25 the manager has plus the $2 the assistant stole equals $27 and if you add the $3 dollars the salesmen got back that makes $30.

The original problem in the telling doesn’t follow the order of operations. Not much in the universe works without it

Mathematics isn’t flawed is what I was getting at... lol