$3$ guys, each with $\$10$ a piece, go to a hotel hoping to get a room to stay in for the night. A room costs $\$60$. The men go in, and ask to rent a room, only having $\$30$ between them. The mater deen says he can give them a broom closet to sleep in for the night. One of the men asks if they can keep a few dollars to get coffee and breakfast in the morning. Mater deen says no, and has a bellboy take them to the closet. Downstairs, the mater deen feels bad, and gives the bell boy $\$5$ to give back to them. The bellboy pockets $2$ of the $5$, and gives each guy a dollar back. IF the men, then, spent $\$9$ each for the closet, and $3\times9 = 27$. The bell boy pocketed $2$, so $27+2=29$. what happened to the $30$th dollar?
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Your double counting the bellboy money. It's money spent by the men then you add that money again to total money spent. – dpmcmlxxvi Jul 22 '15 at 00:42
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After all cash paid and received, these are the modifications of everyone's cash balances:
Hotel +\$25
Men -\$27
Bellboy +\$2
These amounts add to a net change of \$0.
Note that whole the men have paid \$27 the hotel has only received \$25. What's deceptive in the problem statement is to somehow suggest that $27 + 2$ is somehow a relevant quantity. It is not. In terms of the payment to the hotel, the hotel has $27 - 2 = 25$, the 'missing' \$2 being the bellboy's coffee.
Hence: no inconsistency, no problem.
Simon S
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