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In how many ways can 45 cents be made using any combination of quarters, dimes, nickels, and pennies?

 Feb 15, 2022
 #1
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q = quarters, d = dimes, n = nickels, p = pennies

 

Only 1 quarter:

1q + 2d

1q + 1d + 2n

1q + 1d + 1n + 5p

1q + 1d + 10p

1q + 4n

1q + 3n + 5p

1q + 2n + 10p

1q + 1n + 15p

1q + 20p

9 ways

 

No quarter:

4d + 1n

4d + 5p

3d + 3n

3d + 2n + 5p

3d + 1n + 10p

3d + 15p

2d + 5n

2d + 4n + 5p

2d + 3n + 10p

2d + 2n + 15p

2d + 1n + 20p

2d + 25p

1d + 7n

1d + 6n + 5p

1d + 5n + 10p

1d + 4n + 15p

1d + 3n + 20p

1d + 2n + 25p

1d + 1n + 30p

1d + 35p

9n

8n + 5p

7n + 10p

6n + 15p

5n + 20p

4n + 25p

3n + 30p

2n + 35p

1n + 40p

45p

 

30 ways

 

30 + 9 = 39 ways

 Feb 15, 2022
edited by Guest  Feb 15, 2022

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