1. Problem statement. Three girls each paid $100$ for a motel room, for a total of $300$. 2. Clerk realizes the correct charge and refund. The clerk realized the correct charge was $250$ and gave $50$ to the attendant to return to the girls. 3. Attendant returns and effective payments. The attendant gave $10$ back to each girl, so each girl effectively paid $90$ and the three together paid $270$. $$3\times 90 = 270$$ 4. Attendant's withholding and room cost. The attendant kept $20$ and the room cost was $250$. 5. Where the mistaken $10$ appears. The incorrect reasoning adds the attendant's $20$ to the $270$ to get $290$, which double-counts the $20$. The correct relation is: $$270 = 250 + 20$$ This equation shows $270$ already includes the $20$ the attendant kept. 6. Final check and answer. Compute the correct subtraction to verify: $$270 - 20 = 250$$ Therefore there is no missing $10$; the apparent missing amount comes from adding when one should subtract. Final answer: No money is missing; $270$ equals the $250$ room charge plus the $20$ kept by the attendant.