The coins, 5 quarters, 3 dimes and 4 nickles only adds up to 
$1.75, so to get $3.50, we must use both dollar bills.

So we must make the remaining $1.50 with the coins.

If we used all 3 dimes and 4 nickles, which makes 50 cents, we could
make the remaining $1.00 by using 4 quarters.  That's one way.

1.  two $1 bills, 4 quarters, 3 dimes and 4 nickles.

If we use all 5 quarters, we would need 25 cents more using
dimes and nickles.  There are two ways to have that, 2 dimes
and 1 nickle or 1 dime and 3 nickles.

2. two $1 bills, 5 quarters, 2 dimes and 1 nickle.
3. two $1 bills, 5 quarters, 1 dime and 3 nickles. 

So there are three ways.

Edwin