Expert: Steve Holleran - 5/5/2007

Question
In how many ways can 79$ be paid exactly using only 5$ bills and 2$ coins?


Answer
Hi David,

Okay, seems to me the easiest way to do this is to make a table.   I suggest something like listing the $5 bills and $2 coins in a column, and start with the first workable number or $2 coins: you can't use one $2 coin, because then you'd have to make up $77 with $5 bills, and it can't be done.  With 2 -$2 coin, that leaves $75, and you can use 15 - $5 bills.  After that, you need to use 5 more $2 coins to get an amount that can be made up of $5 bills.
The pattern is below:

            $2            $5
       -------------------------

            2              15

            7              13

            12             11

            17              9

            22              7

            27              5

            32              3

            37              1

I hope this helps you out.

Steve Holleran