Math help? 10 points!

How many different combinations of quaters,nickles,and dimes can be used to make $0.55?

First think about your possible coin options: quarter = .25, dime = .10, nickle = .05
Lets start with quarters, you can either have 2 quarters or 1 quarter.
2q + 1n = 55
1q + 3d = 55
1q + 2d + 2n = 55
1q + 1d + 4n = 55
1q + 6n = 55
All possible quarter combos
Next dimes
5d + 1n = 55
4d + 3n = 55
3d + 5n = 55
2d + 7n = 55
1d + 9n = 55
All dime combos
finally nickles
11n = 55

so 11 possible combos

Instructions

1
Place one quarter on a table to equal 25 cents. Add two nickels to the quarter to equal 35 cents. Add two dimes to the other coins to equal 55 cents.

2
Start with one quarter on a table to equal 25 cents. Add four nickels to the quarter to equal 45 cents. Add one dime to the other coins to equal 55 cents.

3
Begin with one quarter. Add six nickels to the quarter to equal 55 cents or add three dimes to the quarter to equal the same sum.

4
Start with two quarters, equaling 50 cents. Add one nickel to the quarters to equal 55 cents. You could also place 11 nickels out or five dimes and one nickel to equal 55 cents.

q= Qarters n= Nickels d= Dimes
2q 1n
1q 3d
11n
9n 1d
7n 2d
1q 6n
5n 3d
1q 2n 2d
1q 4n 1d
5d 1n
4d 3n

1) 11n
2) 9n+1d
3) 7n+2d
4) 5n+3d
5) 3n+4d
6) 1n+5d
7) 2q+1n
8) 1q+6n
9) 1q+3d
10) 1q+2d+2n
11) 1q+1d+4n

11 combos
2 if it has to be Qs AND Ns AND Ds