Need some math assistance

I have heard/read this problem before and I find it very frustrating because it has very little to do with math and yet it is often offered as a mathematical exercise. The real crux of this problem is in the wording "...how much did the store actually lose?" This is vague and ambiguous at best and out of touch with reality at worst. If the intended question was "...how much MONEY did the store actually lose?" The most accurate answer should include there was $30 lost as well as merchandise worth approximately $70 (which if we assume 30% mark up that is normal in retail only cost the store $53.85.) Of course, taxes are never mentioned in this so we have no clue if sales tax was paid or not on the $70 purchase and that could be $15 or more in many states This leads to over 20% error if we just stick to those nice multiples of $10 offered as solutions. The problem does not even account for insurance claim costs and litigation costs if the owner was silly enough to report this loss to the police instead of just eating the loss. 

There was $100 lost but that same $100 was given back and $30 was returned as well as the merchandise. So in this problem's fictional world that does not make any sense at all, they probably wanted the student to answer $30 as the "correct" answer. Since we are not given any information about what the profit margin was on that $70 purchase, nor are we given any tax information on the purchase there is no way to determine how much over $30 was lost but one could assume it was at least $50 - $60 more in lost inventory or $80- $90 retail (including a reasonable sales tax). $30 + merchandise lost gives us a number in the range of $80 - $120. So, if your learner was talking about real world situations, the guess of $100 makes the most sense, but he/she would sadly be marked incorrect because the original author did not construct a question to meet his or her intent well. 

This is so frustrating because if we would approach the learner with monopoly money and give $100 to them and have them physically exchange bills for them to discover how much money was actually lost. They would see that $30 could and probably is what the answer key has. Bringing up the whole value of the lost merchandise could be a teachable moment to talk about the real retail world, profit margins, taxes, insurances and the real cost of theft in the retail world, but this would bring up the same test frustration in the learner that you may be reading in my tone. So do we teach to the test to keep the learner blissfully ignorant of what real world aspects are, or do we teach to the real world and demonstrate the foolish nature of most standardized "real world" questions asked in mathematics?

I don't know what the original author intended to assess, and this question has been floating around Facebook for a good amount of time, but I would love to know what the intent was so we could actually construct wording that better hits the intent. Was this a simple play on words "joke" or was this really intended as a sort of logic problem or was it intended to be a basic computational math problem. Should this problem have asked "...how much cash did the store loose, not counting the value of the merchandise stolen?" ? Even then there is still $15 or so in taxes on that $70 purchase unaccounted for, (depending on the state rate this happened in). 

I am sorry for the frustrated response, but I am getting to be a crabby old man when it comes to math problems that hint at being real world but are so out of touch with what actual situations are in the real world. Our elementary text, high school text, and college texts are so full of ridiculous application problems that frustrate adults that actually live and work in the real world. I get carpenters asking me about math carpenter questions, "Why the @#$@ would anyone do this? In the field I just do .... and I am done. This is stupid." We have proficient adults in our programs fully capable of processing mathematics that are getting totally baffled by horrible word problems in academics. I am frustrated that the mathematics community has not pressured the for profit text companies to provide more realistic application problems for our adult learners. I am aware there are some agencies attempting to do just that, but this problem has persisted for decades, if not longer. 

Sorry again for the rant. I am repeating the accumulated frustration that adult learners bring to me every day as they approach our academic math worlds and I wish exposure and discussion of good problem design picks up steam and starts to offer improvements. Otherwise, the study of mathematics, as presented in academic word problems is nothing more than a joke or trivia to our learners. 

As Edward stated, the problem with this question is the wording - you're missing a key piece of information which is the profit margins or perhaps more accurate;y the markup for the goods that were paid for with the stolen $100 bill. 

With that said, I would assume that this problem is trying to get you to $100 as the store effectively lost $70 worth of merchandise and $30 cash when the thief returned and paid for the goods with the stolen $100 bill.

There's been a discussion on Quora about this question as well that you might find useful.