SOLUTION: $4.65 in change, but I have 3 more quarters than dimes but 4 times as many nickels as quarters. how many total?

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Question 512667: $4.65 in change, but I have 3 more quarters than dimes but 4 times as many nickels as quarters. how many total?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
There are 50 different solutions to this problem.
Here they all are, counting the cases where there are 
no dimes and 3 quarters, since 3 quarters is 3 more 
coins than no dimes or 0 dimes. 

 1. 3 quarters, 12 nickels, 330 pennies.
 2. 4 quarters, 1 dime, 16 nickels, 275 pennies.
 3. 5 quarters, 2 dimes, 20 nickels, 220 pennies.
 4. 6 quarters, 3 dimes, 24 nickels, 165 pennies.
 5. 7 quarters, 4 dimes, 28 nickels, 110 pennies.
 6. 8 quarters, 5 dimes, 32 nickels, 55 pennies.
 7. 9 quarters, 6 dimes, 36 nickels.
 8. 1 half dollar, 3 quarters, 12 nickels, 280 pennies.
 9. 1 half dollar, 4 quarters, 1 dime, 16 nickels, 225 pennies.
10. 1 half dollar, 5 quarters, 2 dimes, 20 nickels, 170 pennies.
11. 1 half dollar, 6 quarters, 3 dimes, 24 nickels, 115 pennies.
12. 1 half dollar, 7 quarters, 4 dimes, 28 nickels, 60 pennies.
13. 1 half dollar, 8 quarters, 5 dimes, 32 nickels, 5 pennies.
14. 2 half dollars, 3 quarters, 12 nickels, 230 pennies.
15. 2 half dollars, 4 quarters, 1 dime, 16 nickels, 175 pennies.
16. 2 half dollars, 5 quarters, 2 dimes, 20 nickels, 120 pennies.
17. 2 half dollars, 6 quarters, 3 dimes, 24 nickels, 65 pennies.
18. 2 half dollars, 7 quarters, 4 dimes, 28 nickels, 10 pennies.
19. 3 half dollars, 3 quarters, 12 nickels, 180 pennies.
20. 3 half dollars, 4 quarters, 1 dime, 16 nickels, 125 pennies.
21. 3 half dollars, 5 quarters, 2 dimes, 20 nickels, 70 pennies.
22. 3 half dollars, 6 quarters, 3 dimes, 24 nickels, 15 pennies.
23. 4 half dollars, 3 quarters, 12 nickels, 130 pennies.
24. 4 half dollars, 4 quarters, 1 dime, 16 nickels, 75 pennies.
25. 4 half dollars, 5 quarters, 2 dimes, 20 nickels, 20 pennies.
26. 5 half dollars, 3 quarters, 12 nickels, 80 pennies.
27. 5 half dollars, 4 quarters, 1 dime, 16 nickels, 25 pennies.
28. 6 half dollars, 3 quarters, 12 nickels, 30 pennies.
29. 1 dollar coin, 3 quarters, 12 nickels, 230 pennies.
30. 1 dollar coin, 4 quarters, 1 dime, 16 nickels, 175 pennies.
31. 1 dollar coin, 5 quarters, 2 dimes, 20 nickels, 120 pennies.
32. 1 dollar coin, 6 quarters, 3 dimes, 24 nickels, 65 pennies.
33. 1 dollar coin, 7 quarters, 4 dimes, 28 nickels, 10 pennies.
34. 1 dollar coin, 1 half dollar, 3 quarters, 12 nickels, 180 pennies.
35. 1 dollar coin, 1 half dollar, 4 quarters, 1 dime, 16 nickels, 125 pennies.
36. 1 dollar coin, 1 half dollar, 5 quarters, 2 dimes, 20 nickels, 70 pennies.
37. 1 dollar coin, 1 half dollar, 6 quarters, 3 dimes, 24 nickels, 15 pennies.
38. 1 dollar coin, 2 half dollars, 3 quarters, 12 nickels, 130 pennies.
39. 1 dollar coin, 2 half dollars, 4 quarters, 1 dime, 16 nickels, 75 pennies.
40. 1 dollar coin, 2 half dollars, 5 quarters, 2 dimes, 20 nickels, 20 pennies.
41. 1 dollar coin, 3 half dollars, 3 quarters, 12 nickels, 80 pennies.
42. 1 dollar coin, 3 half dollars, 4 quarters, 1 dime, 16 nickels, 25 pennies.
43. 1 dollar coin, 4 half dollars, 3 quarters, 12 nickels, 30 pennies.
44. 2 dollar coins, 3 quarters, 12 nickels, 130 pennies.
45. 2 dollar coins, 4 quarters, 1 dime, 16 nickels, 75 pennies.
46. 2 dollar coins, 5 quarters, 2 dimes, 20 nickels, 20 pennies.
47. 2 dollar coins, 1 half dollar, 3 quarters, 12 nickels, 80 pennies.
48. 2 dollar coins, 1 half dollar, 4 quarters, 1 dime, 16 nickels, 25 pennies.
49. 2 dollar coins, 2 half dollars, 3 quarters, 12 nickels, 30 pennies.
50. 3 dollar coins, 3 quarters, 12 nickels, 30 pennies.
 
Edwin