Sharing Money

Date: 01/25/97 at 16:16:29
From: Mike
Subject: Coin problem

Mark has 2 quarters, three nickels, and three pennies.  Juanita has 
1 quarter, two dimes, and a penny.  Frank has 1 half-dollar and 4 
pennies.  How can Mark, Juanita, and Frank share the coins so that 
each has the same amount of money?

Date: 01/25/97 at 18:08:23
From: Doctor Wallace
Subject: Re: Coin problem

Hi Mike!

The first thing to do in this problem is to find out, after they have 
shared the coins, how much money each will have.  To do this, we only 
need to average by adding up how much money they have and dividing it 
equally among them.

Mark has 2 quarters, 3 nickels, and 3 pennies = 68 cents
Juanita has 1 quarter, 2 dimes, and a penny   =  46 cents
Frank has 1 half-dollar and 4 pennies         = 54 cents

So, 68 + 46 + 54 = $1.68.  If we divide this by 3, we get 56 cents.

So, we want each of them to have 56 cents.  Now what we have to do is 
come up with combinations of coins that total 56 cents.  What you need 
to do is list all the combinations of these coins that could make 56 
cents.  I'll get you started.

Let's look at the half-dollar.  It is already worth 50 cents.  So we 
have to add six more cents.  There are only two ways to do this, given 
our coins.  We can use 6 pennies, or 1 nickel and 1 penny.  So these 
are your first two combinations:   

     (1)  The half-dollar, 1 nickel, and 1 penny
     (2)  The half-dollar and 6 pennies

Since you know that all the coins have to be used, one of the three 
people will get the half-dollar, so one and only one of these two 
combinations will be used in the final answer, not both.

Next, go to the quarters.  How can you make 56 cents using the 
quarters?  Well, there are 3, but we can't use all three, since that 
would be 75 cents.  But we can use 2.  That's 50 cents again.  So we 
again can use 1 nickel and 1 penny or 6 pennies.

It may seem like there are a lot of combinations to list, but there 
are not.  For example, you can't make 56 cents unless you use at least 
1 of the three quarters, so you can rule out any combination of just 
dimes, nickels, and pennies.

After you list all the combinations, you can start seeing which ones 
will work together.  For example, we couldn't put six pennies with the 
half-dollar and also with 2 quarters since we only have 8 pennies 
total.  Then you can assign one to each of the three people and you're 
done!

I hope this helps.  If you need more hints, feel free to write back!  

-Doctor Wallace,  The Math Forum
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