The individual people cause this mess...
The group paid $30 (yes is 10 per person. That's NOT important) Then they get 5 back. Now they've paid $25 (8.34 per person). The bellboy takes $2. NOW they have paid $27 (25+2). So, now each had paid $9. BUT the manager paid out $5. So, where is it? The bellboy has $2 of it, the group gets the other $3. Make sense?
This is a common paradox puzzle:
The Missing $
Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 is difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totaling $29. Where is the missing $?
ADK