SOLUTION: a child's bank contains $1.15 in dimes and quarters. Find all the possibilities for the number of each type of coin in the bank

Since $1.15 ends with a 5, the bank cannot contain exactly
2 quarters or exactly 4 quarters, because adding any number
of dimes to 2 or 4 quarters will only give a sum ending 
in 0.  So there can only either be exactly 1 or exactly 3 
quarters.

So there are just 2 possibilities:

If there is exactly 1 quarter, the remaining 90¢ must consist of 9 dimes.
If there are exactly 3 quarters, the remaining 40¢ must consist of 4 dimes.

Edwin