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 
class is divided on the answer, so I am asking for your help. 

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:

    Buyer         Shoestore Owner         Grocer           FBI
      -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/