How much did the owner lose if a woman walks into a store and steals 100 out of the register and comes back 5 minutes later and buys 70 worth of groceries and gets 30 in change?

Answer 1

Scenario 1: The woman paid with the $100 she stole

If the woman paid with the $100 she stole, the owner lost $100. The woman bought $70 of groceries with his money and then received $30 in change. Work the question out step by step:

First, the woman takes $100 dollars from the register.

The owner has currently lost $100.

Second, the woman buys $70 worth of groceries. But it's not her money she's going to pay with, so it's another $70 stolen.

The owner has currently lost $170.

The lady pays the teller $100. That's stolen, so she is giving the $100 back to the owner.

The owner has currently lost $70.

Finally, the woman receives $30 back in change. She paid with the owner's money, so the owner is giving her $30.

The owner lost $100.

Scenario 2: The woman returned with her own $100

However, if the woman brought in her own $100, the owner would have still lost $100 because she stole $100 and paid with her own money. Work it out:

First, the woman steals $100 from the register.

The owner has lost $100.

Second, the woman comes back and is going to buy $70 of groceries with her own $100. She has not yet paid for it.

The owner has lost $170.

The lady pays the teller $100. This is her own money, so the teller gains $100.

The owner has lost $70.

Finally, the woman receives $30 back in change.

The owner has lost $100.

Scenario 3: The woman returns with a counterfeit $100

A third scenario would be that the woman returned with a counterfeit $100. If that is the case, then the owner lost $200.

• First, $100 were stolen from the register.
• Second, $70 were bought with fake money
• Third, $30 were given in exchange for fake money

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This is an interesting question and could depend on how you define "lost". Personally I would define the loss to the vendor as the amount required to give redress, ie put them back in the situation before the theft. Working through the transactions (assuming legal tender at all times) gives:

Theft for $100 - vendor has lost $100

Thief pays $100 to vendor - vendor has lost $0

Vendor gives $30 change - vendor has lost $30

Vendor lets thief take away goods with a sales price including sales tax of $70 - vendor has lost the cost price of the goods and must pay the sales tax to the government.

Thus the actual loss is $30 + cost of goods taken + sales tax on the sales price of those goods - this is the amount that the vendor would need to receive to put them back to the situation before the theft from the till took place.

There is also an opportunity cost which is the potential profit that the vendor would have made on the sale of those goods: loss + potential profit = $100.

Another way to see what has happened:

It is often easier to look at a problem if it is either reduced to the minimum or expanded ridiculously. In this case, if we reduce the problem to the minimum, then we consider the vendor making only this sale (having for some unknown reason left lots of money in the till).

After this transaction we know:

• cost of goods
• sales price of goods (assume greater than cost as normally goods are sold for a profit)
• sales tax on goods: some percentage of sales price which is money that has to be paid to the government; total paid to vendor is sales price = sales tax
• money received (less change): $100 - $30 = $70
• money stolen: $100

The profit(/loss) on the sale is: sales_price - cost_price

money paid to government: sales_tax

After the theft is discovered: final profit = sales_price - cost_price - $100

A loss is a negative profit, so the loss is -(sales_price - cost_price - $100) = $100 + cost_price - sales_rice

The money received is sales price + sales tax, thus:

sales_price + sales_tax = $70

→ sales_price = $70 - sales_tax

Substituting this for sales price in the final loss gives:

→loss = $100 + cost_price - sales_price

= $100 + cost_price - ($70 - sales_tax)

= $100 + cost_price - $70 + sales_tax

= $30 + cost of goods + sales tax

as the next amount of money the vendor has had to pay out for this transaction - in other words the loss of this transaction to the vendor.

Answer 2

One way of looking at it would be that the owner lost 100 "monies" (you didn't specify the currency unit). Alternatively, the owner lost 30 monies plus 70 monies worth of goods, which almost certainly cost him less than 70 monies to buy, though on the other hand there is overhead involved with inventory and storage and cost of sale ... 100 monies is the simplest answer.

Answer 3

The 100 that were stolen - minus any profit the owner might have made on the sale, if you want to take that into account.