Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the remaining dollar?

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Now each person paid $10 and got back $1. So they paid $9 each, totalling $27."

The people paid BOTH the hotel room bill AND (unknowingly) the bellboy $27 total ($25 + $2). $25 charged for the hotel room; $2 kept by bellboy

What isn't accounted for yet is the $3 the people got back.

"The bellboy has $2, totalling $29."

$2 was already accounted for in the $27. Why add it again?

"Where is the missing $1?"

Nothing is missing. Complete the accounting with $27 (hotel AND bellboy) + $3 (change from $30) = $30 (money originally paid by the people)

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ADDITIONAL-

If you like it better:

per person: ($8+$1/3) share of room charge + ($2/3) secret bellboy tax + ($1) refunded = $10 originally paid amount.

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