Subjects algebra

Motel Room Riddle

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Motel Room Riddle


1. **State the problem:** Three girls paid $100 each, totaling $300, for a motel room. The clerk later realizes the correct charge should be only $250, so he gives $50 to the attendant to return. 2. **What happens next:** The attendant gives $10 back to each girl (total $30) and keeps $20. Now, each girl has effectively paid $90 ($100 - $10), totaling $270. 3. **The confusion:** It is said that the girls paid $270 and the attendant has $20, which sums to $290. People then ask, what happened to the other $10? 4. **Step-by-step analysis:** - Total amount originally paid: $300 - Correct room price: $250 - Refund to girls: $30 ($10 each) - Attendant keeps: $20 5. **Clarify the addition mistake:** The $270 paid by the girls already **includes** the $20 with the attendant (since $270 = $250 (room) + $20 (attendant)). Adding the attendant's $20 again to $270 is incorrect. 6. **Correct way to account:** Girls' payment ($270) = Room cost ($250) + Attendant's kept money ($20) The $30 refund is already deducted from their original $300. 7. **Summary:** There is no missing $10. The misdirection comes from adding the $270 paid and the $20 held by the attendant, which double counts the $20. **Final answer:** No money is missing. The $270 includes the $20 held by the attendant, and the room cost is $250.