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### 5 Coins = 55 Cents

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Date: 01/28/97 at 22:04:44
From: Sara
Subject: Five coins = 55 cents

I have five coins in my pocket. together they are worth 55 cents.
What coins do I have?
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```
Date: 01/29/97 at 12:30:54
From: Doctor Wilkinson
Subject: Re: Five coins = 55 cents

Let's think about it.  First of all, you must have at least one
quarter, because 5 dimes would only make 50 cents.

You can't have two quarters, because that would make 50 cents.  If you
also had a nickel, then that would be 55 cents in just 3 coins, but if
you just had pennies, 3 of them would only make 53 cents.

So you must have just one quarter.  That leaves four coins to make 30
cents from.

Now you need at last one dime, because four nickels would only make 20
cents.

In fact you need two dimes, because if you just had one dime, you
would have to make 20 cents out of just three coins, and three nickels
would only give you 15 cents.

So now you have a quarter and two dimes, which is 45 cents.  You need
to make the remaining 10 cents out of two coins, and two nickels is
the only possibility.

So you have one quarter, two dimes, and two nickels.

-Doctor Wilkinson,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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