1. **Stating the problem:** Three girls paid 100 each, totaling 300, for a motel room. The correct charge was 250, so the clerk gave 50 to the attendant to return. The attendant gave 10 back to each girl and kept 20. Now, the girls paid 90 each (total 270), and the attendant has 20. The question is: where is the missing 10? 2. **Analyzing payments and refunds:** - Total paid originally: $300 - Correct charge: $250 - Amount to return: $50 - Attendant returns $10 each to three girls: total $30 - Attendant keeps $20 3. **Examining the money flow:** - Girls effectively paid $90 each, so total $270 - This $270 is the $250 room charge plus $20 that the attendant kept - So, $270 = $250 + $20, no money is missing 4. **Explaining the misconception:** The problem’s error is adding the attendant's $20 to the $270 paid by the girls as if they should sum to $300. In reality, the $270 already includes the attendant's $20. The correct accounting is: $$\text{Total paid by girls} = \text{Cost of room} + \text{money kept by attendant}$$ $$270 = 250 + 20$$ The $30 returned ($10 each) plus the $270 paid equals the original $300. 5. **Conclusion:** There is no missing $10. The confusion arises from incorrect addition of the attendant’s $20 to the girls’ total payment instead of including it within. **Final answer:** The missing $10 does not exist; the accounting method in the problem is misleading.