Question: Three girls paid $100 each, a total of $300, to share a motel room. Later, the desk clerk realizing she should have only charged $250, gives the room attendant $50 and asks him to return it to the three girls. Unable to divide the money three ways he decides to give $10 to each girl and pockets the remaining $20. The girls have now paid $90 each or $270 for the room, and the room attendant has $20. What happened to the other $10?

1. **State the problem:** Three girls initially pay $100$ each, totaling $$300$$, for a motel room. The correct charge is $$250$$, so the clerk gives $$50$$ to the attendant to return to the girls. The attendant gives $$10$$ back to each girl (total $$30$$) and keeps $$20$$. 2. **Analyze the payments:** - Each girl effectively paid $$100 - 10 = 90$$ dollars. - Total paid by the girls is $$3 \times 90 = 270$$ dollars. - The attendant has $$20$$ dollars. 3. **Clarify the confusion:** The statement "The girls have now paid $$270$$ and the attendant has $$20$$" adds these amounts incorrectly: $$270 + 20 = 290$$ This sum is misleading because the $$20$$ is part of the $$270$$ total paid by the girls, not in addition to it. 4. **Break down the $$270$$:** - $$250$$ went to the motel for the room. - $$20$$ is with the attendant. So, $$270 = 250 + 20$$ 5. **The missing $$10$$:** The $$10$$ is not missing; it is the $$30$$ returned to the girls minus the $$20$$ kept by the attendant: $$30 - 20 = 10$$ But more precisely, the $$10$$ is part of the $$30$$ returned to the girls, so the total money is accounted for: - Girls paid $$270$$ - Girls got back $$30$$ - Motel kept $$250$$ - Attendant kept $$20$$ 6. **Conclusion:** The error is in adding the $$20$$ to the $$270$$ instead of subtracting it or understanding it is included in the $$270$$. There is no missing $$10$$. **Final answer:** The other $$10$$ does not exist; the confusion arises from incorrect addition of the amounts.