Answer: 11
Explanation:
If you use 0 dimes, you can use 11 nickels.
If you use 1 dime, you can use 9 nickels.
A chart develops:
0 11
1 9
2 7
3 5
4 3
5 1
So there are 6 ways to make 55 cents with nickels and dimes alone.
Now for the situation with 1 quarter:
We can have 0 dimes and 6 nickels.
We can have 1 dime and 4 nickels.
A chart follows:
0 6
1 4
2 2
3 0
So there are 4 ways to make change with nickels and dimes and 1 quarter.
Finally, if we use 2 quarters, we have 5 cents left over which must be a nickel adding 1 more way.
So there are 6 + 4 + 1 ways = 11 total ways to make 55 cents with nickels dimes and quarters.