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/
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