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### Counterfeit Money

```
Date: 05/28/99 at 11:32:13
From: Cassie Bishop
Subject: Counterfeit money

A man goes into a shoestore and buys a pair of shoes for \$5. He pays
with a counterfeit \$20 bill but the shoestore owner does not realize
it. Not having change for the \$20 bill, the owner runs to the grocer
next door. The grocer gives the shoestore owner four \$5 bills and the
shoestore owner gives the man the shoes and \$15 change.

Later the grocer comes back to the shoestore owner with the FBI and
informs him that the \$20 bill was counterfeit, so the shoestore owner
gives the grocer \$20, and the FBI keeps the counterfeit bill.

How much did the shoestore owner lose?

This is all of the information we have been supplied. Our Algebra

Cassie Bishop
```

```
Date: 05/28/99 at 12:22:29
From: Doctor Peterson
Subject: Re: Counterfeit money

Hi, Cassie.

You can diagram the situation this way, with C for the counterfeit
bill and S for the shoes:

-C   --------->   +C
-C  ------------>  +C
+\$20 <------------ -\$20
+S+\$15 <--------- -S-\$15
-\$20 ------------> +\$20
-C  ----------> +C
========          ======              ====             ==
-C+S+\$15          -S-\$15               +0              +C

Let's think about what everyone has gained or lost:

The buyer lost a counterfeit bill, and gained a pair of shoes and \$15.

The shoestore lost a pair of shoes and \$15 (the counterfeit bill just
passed through, and the extra \$20 just paid for the 4 \$5 bills).

The grocer came out even.

The FBI gained a counterfeit bill.

Technically, the shoestore didn't lose \$20, since the shoes didn't
actually cost the store \$5. We can't say how much money they actually
lost; but I notice the question didn't ask how much money, just how
much. Smart!

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
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