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There are 22 ways to make change from a dollar using nickels, dimes, and quarters.

1. 4 q

2. 10 d

3. 20 n

4. 2 q , 5 d

5. 3 q , 2 d , 1 n

6. 1 q , 7 d, 1 n

7. 9 d, 2 n

8. 8 d, 4 n

9. 7 d, 6 n

10. 6 d , 8 n

11. 5 d , 10 n

12. 4 d , 12 n

13. 2 d , 16 n

14. 1 d , 18 n

15. 5 n , 3 q

16. 3 n , 1 q , 6 d

17. 7 n , 1 q , 4 d

18. 9 n , 1 q , 3 d

19. 11 n , 1 q , 2 d

20. 13 n , 1 q , 1 d

21. 14n , 3 d

22. 15n , 1 q

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In how many ways can you make change for 75 cents using nothing but nickels andor dimes?

To make change for 75 cents using only nickels (5 cents) and dimes (10 cents), we can express the total amount in terms of the number of each coin. Let ( n ) be the number of nickels and ( d ) be the number of dimes. The equation is ( 5n + 10d = 75 ) or simplified as ( n + 2d = 15 ). The values of ( d ) can range from 0 to 7 (since ( 2d ) must be less than or equal to 15), which gives us 8 possible values for ( d ) (0 through 7), leading to a total of 8 combinations of nickels and dimes.


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