Question 238138
What number of quarters, dimes, nickles and pennies add up to 1 dollar. You need at least one of each type of coin. Can you do this as an equation and not using "trial and error"?
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Not as an equation. But here are all 60 ways:

1. 1 quarter, 1 dime, 1 nickle and 60 pennies.
2. 1 quarter, 1 dime, 2 nickles and 55 pennies.
3. 1 quarter, 1 dime, 3 nickles and 50 pennies.
4. 1 quarter, 1 dime, 4 nickles and 45 pennies.
5. 1 quarter, 1 dime, 5 nickles and 40 pennies.
6. 1 quarter, 1 dime, 6 nickles and 35 pennies.
7. 1 quarter, 1 dime, 7 nickles and 30 pennies.
8. 1 quarter, 1 dime, 8 nickles and 25 pennies.
9. 1 quarter, 1 dime, 9 nickles and 20 pennies.
10. 1 quarter, 1 dime, 10 nickles and 15 pennies.
11. 1 quarter, 1 dime, 11 nickles and 10 pennies.
12. 1 quarter, 1 dime, 12 nickles and 5 pennies.
13. 1 quarter, 2 dimes, 1 nickle and 50 pennies.
14. 1 quarter, 2 dimes, 2 nickles and 45 pennies.
15. 1 quarter, 2 dimes, 3 nickles and 40 pennies.
16. 1 quarter, 2 dimes, 4 nickles and 35 pennies.
17. 1 quarter, 2 dimes, 5 nickles and 30 pennies.
18. 1 quarter, 2 dimes, 6 nickles and 25 pennies.
19. 1 quarter, 2 dimes, 7 nickles and 20 pennies.
20. 1 quarter, 2 dimes, 8 nickles and 15 pennies.
21. 1 quarter, 2 dimes, 9 nickles and 10 pennies.
22. 1 quarter, 2 dimes, 10 nickles and 5 pennies.
23. 1 quarter, 3 dimes, 1 nickle and 40 pennies.
24. 1 quarter, 3 dimes, 2 nickles and 35 pennies.
25. 1 quarter, 3 dimes, 3 nickles and 30 pennies.
26. 1 quarter, 3 dimes, 4 nickles and 25 pennies.
27. 1 quarter, 3 dimes, 5 nickles and 20 pennies.
28. 1 quarter, 3 dimes, 6 nickles and 15 pennies.
29. 1 quarter, 3 dimes, 7 nickles and 10 pennies.
30. 1 quarter, 3 dimes, 8 nickles and 5 pennies.
31. 1 quarter, 4 dimes, 1 nickle and 30 pennies.
32. 1 quarter, 4 dimes, 2 nickles and 25 pennies.
33. 1 quarter, 4 dimes, 3 nickles and 20 pennies.
34. 1 quarter, 4 dimes, 4 nickles and 15 pennies.
35. 1 quarter, 4 dimes, 5 nickles and 10 pennies.
36. 1 quarter, 4 dimes, 6 nickles and 5 pennies.
37. 1 quarter, 5 dimes, 1 nickle and 20 pennies.
38. 1 quarter, 5 dimes, 2 nickles and 15 pennies.
39. 1 quarter, 5 dimes, 3 nickles and 10 pennies.
40. 1 quarter, 5 dimes, 4 nickles and 5 pennies.
41. 1 quarter, 6 dimes, 1 nickle and 10 pennies.
42. 1 quarter, 6 dimes, 2 nickles and 5 pennies.
43. 2 quarters, 1 dime, 1 nickle and 35 pennies.
44. 2 quarters, 1 dime, 2 nickles and 30 pennies.
45. 2 quarters, 1 dime, 3 nickles and 25 pennies.
46. 2 quarters, 1 dime, 4 nickles and 20 pennies.
47. 2 quarters, 1 dime, 5 nickles and 15 pennies.
48. 2 quarters, 1 dime, 6 nickles and 10 pennies.
49. 2 quarters, 1 dime, 7 nickles and 5 pennies.
50. 2 quarters, 2 dimes, 1 nickle and 25 pennies.
51. 2 quarters, 2 dimes, 2 nickles and 20 pennies.
52. 2 quarters, 2 dimes, 3 nickles and 15 pennies.
53. 2 quarters, 2 dimes, 4 nickles and 10 pennies.
54. 2 quarters, 2 dimes, 5 nickles and 5 pennies.
55. 2 quarters, 3 dimes, 1 nickle and 15 pennies.
56. 2 quarters, 3 dimes, 2 nickles and 10 pennies.
57. 2 quarters, 3 dimes, 3 nickles and 5 pennies.
58. 2 quarters, 4 dimes, 1 nickle and 5 pennies.
59. 3 quarters, 1 dime, 1 nickle and 10 pennies.
60. 3 quarters, 1 dime, 2 nickles and 5 pennies.


Edwin</pre>