Posted by **John** on Saturday, March 6, 2010 at 5:15am.

How many different sums of money can be formed from one $2 bill, three $5 bills, two $10 bills, and one $20 bill?

the answer at the back of the book is 23, but i don't know how to solve it.

- Data Management -
**MathMate**, Saturday, March 6, 2010 at 9:25am
We note that the question requires different sums of money, irrespective of how they are made up, it is important not to double count. For example 1-$10 and 2-$5 bills should be counted as one sum.

Start with the multiples, namely the $5, $10, and $20 bills. The possible sums range from $0 to $55 in $5 increments. That makes 12 possible sums.

By adding a $2 bill, we get 12 more sums, namely from $7 to $57 in $5 increments. This makes a total of 24 sums, including $0.

If the question implies at least one bill must be used, then there are 23 sums.

- Data Management -
**John**, Sunday, March 7, 2010 at 8:37pm
is there a formula for this?

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