Data Management
posted by John on .
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.

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. 
is there a formula for this?