Making Change

Date: 04/15/99 at 00:25:01
From: Jeffrey Mo
Subject: Perimeter/Area/Volume, word problem

1. John has a pocket full of change, yet he can't make change for a 
   dollar, a half-dollar, a quarter, a dime, or a nickel. What is the 
   greatest amount of money John can have in his pocket?

Date: 04/15/99 at 11:19:54
From: Doctor Rob
Subject: Re: Perimeter/Area/Volume, word problem

Thanks for writing to Ask Dr. Math!

Start by thinking about changing using only one kind of coin. 

   If he had 5 or more pennies, he could change a nickel, so he has 
at most 4.  

   If he had 2 or more nickels, he could change a dime, so he has 
at most 1. 

   If he had 5 or more dimes, he could change a half-dollar, so he has 
at most 4. 

   If he had 2 or more quarters, he could change a half-dollar, so he 
has at most 1. 

   If he had 2 or more half-dollars, he could change a dollar, so he 
has at most 1.

Now you have to deal with the possibilities of changing using two or
more kinds of coins. 

Four or fewer pennies will not help changing anything, so you might as 
well give him the four pennies. 

One nickel and two dimes will change a quarter, so if he has 1 nickel, 
he has at most 1 dime. If he has no nickel, he has at most 4 dimes.

Now put all this together.

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