You can
put this solution on YOUR website!
We can use either 0, 1, 2, 3, or 4 quarters.
If we use 0 quarters, we can use from 0 up to 10 dimes,
and the rest, if any, in nickels. That accounts for 11 ways.
If we use 1 quarter, we can use from 0 up to 7 dimes,
and the rest in nickels. That accounts for 8 ways.
If we use 2 quarters, we can use from 0 up to 5 dimes,
and the rest, if any, in nickels. That accounts for 6 ways.
If we use 3 quarters, we can use from 0 up to 2 dimes,
and the rest in nickels. That accounts for 3 ways.
If we use 4 quarters, that's the whole dollar, so that accounts
for 1 way.
So the total number of ways = 11+8+6+3+1 = 29
You weren't asked to list them, but here is the
list of all 29 ways:
1. 0 quarters, 0 dimes, and 20 nickels.
2. 0 quarters, 1 dime, and 18 nickels.
3. 0 quarters, 2 dimes, and 16 nickels.
4. 0 quarters, 3 dimes, and 14 nickels.
5. 0 quarters, 4 dimes, and 12 nickels.
6. 0 quarters, 5 dimes, and 10 nickels.
7. 0 quarters, 6 dimes, and 8 nickels.
8. 0 quarters, 7 dimes, and 6 nickels.
9. 0 quarters, 8 dimes, and 4 nickels.
10. 0 quarters, 9 dimes, and 2 nickels.
11. 0 quarters, 10 dimes, and 0 nickels.
12. 1 quarter, 0 dimes, and 15 nickels.
13. 1 quarter, 1 dime, and 13 nickels.
14. 1 quarter, 2 dimes, and 11 nickels.
15. 1 quarter, 3 dimes, and 9 nickels.
16. 1 quarter, 4 dimes, and 7 nickels.
17. 1 quarter, 5 dimes, and 5 nickels.
18. 1 quarter, 6 dimes, and 3 nickels.
19. 1 quarter, 7 dimes, and 1 nickel.
20. 2 quarters, 0 dimes, and 10 nickels.
21. 2 quarters, 1 dime, and 8 nickels.
22. 2 quarters, 2 dimes, and 6 nickels.
23. 2 quarters, 3 dimes, and 4 nickels.
24. 2 quarters, 4 dimes, and 2 nickels.
25. 2 quarters, 5 dimes, and 0 nickels.
26. 3 quarters, 0 dimes, and 5 nickels.
27. 3 quarters, 1 dime, and 3 nickels.
28. 3 quarters, 2 dimes, and 1 nickel.
29. 4 quarters, 0 dimes, and 0 nickels.
Edwin
