Missing Ten Dollars
1. Let's start by understanding the problem.
Three girls initially pay $100 each, totaling $300.
2. The motel room actually costs $250, so the desk clerk gives $50 to the room attendant to return to the girls.
3. The room attendant gives $10 back to each girl ($30 total), and keeps $20.
4. Now, each girl has effectively paid $90 ($100 - $10), totaling $270.
5. The confusion arises because the problem adds the $20 the attendant kept to the $270 the girls paid, giving $290, which is incorrect.
6. The correct way to account for the money is:
- $250 went to the motel for the room.
- $20 is with the attendant.
- $30 was returned to the girls ($10 each).
7. These add up to $250 + $20 + $30 = $300, the initial amount.
8. The error is in adding the $20 to the $270, instead, the $20 is part of the $270 paid, not in addition to it.
Final answer: There is no missing $10. The mistake is in adding the room attendant's $20 to the total amount paid by the girls, which already includes that $20.