Answer
The owner lose is $100 .
Reason
As given
A man comes into a store and steals $100 from the register without the owner knowledge.
Comes back and buys $70 worth of stuff and the owner gives him $30 in change.
i.e First man steals $100 than give back to owner when he buys $70 worth of stuff and the owner gives him $30 in change.
Therefore the total owner lose is the sum of $70 worth of stuff and $30 in change.
Total owner lose = $70 + $30
= $100
Therefore the owner lose be $100 .
Hence proved