Where'd the other dollar go?

Here's one that has probabaly been on here before, but here goes anyway.

3 traveling salesmen all meet up at a hotel wanting a room. The rate for the night is $15 for a room. Since they are all cheap, they decide to split one room between them. Each pays $5 and go to thier room. ($5 + 5 + 5=$15)

When the manager sees that they are splitting 1 room, he realizes that they quailfied for the hotels group discount which takes $5 off the normal rate. (makeing the room cost $10 a night) He gives the bellhop $5 to take to the three salemen. The bellhop can't decide how to split the $5 evenly between 3 people, so he tells the group that it was only a $3 discount, and gives each man a dollar back, and pockets the remaining $2. Now, lets do the math. Each man paid $5. (5+5+5=15), They each recieved $1 back which means they really only paid $4 a piece, (4+4+4=$12) Now, the bellhop pockets $2, add that to what the men paid and you get $14. The originally paid $15. Where'd the other dollar go?