The Bellhop Problem

[Whateverist]

Ah, but

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the store owner paid less than $70 for the goods

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Realistically, this does need to be considered, so good point. But as a pure math problem/puzzle, do we need to make that assumption, or go with a simplistic one?

The solution is similar to that of the Bellhop puzzle.  

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The calculation of how much of every sale goes to cover overhead, wholesale price of the goods and the margin required to stay in business is entirely separate from the question of how much money the shop owner is out owing to his interaction with the thief.  He is out $100 from the theft of the goods and that is all he is missing.  The later exchange of goods for cash involving the stolen money is status quo from the POV of the shop owner, and shouldn't be mixed up with loss from the theft.

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