how many combinatations to make $10.00 from $0.50, $1.00 and $1.50

Question

Tickets being purchased at a fair, there are $0.50 rides, $1.00 rides and $1.50 rides, Lisa has $10.00 total, how many different ride combinations could she possibly purchase using her total of $10.00?

Answer 1

She could buy any one of the following 44 combinations:

1. 6 rides at $1.50 plus 1 ride at $1
2. 6 rides at $1.50 plus 2 rides at $0.50
3. 5 rides at $1.50 plus 2 rides at $1 plus 1 ride at $0.50
4. 5 rides at $1.50 plus 1 ride at $1 plus 3 rides at $0.50
5. 5 rides at $1.50 plus 5 rides at $0.50
6. 4 rides at $1.50 plus 4 rides at $1
7. 4 rides at $1.50 plus 3 rides at $1 plus 2 rides at $0.50
8. 4 rides at $1.50 plus 2 rides at $1 plus 4 rides at $0.50
9. 4 rides at $1.50 plus 1 ride at $1 plus 6 rides at $0.50
10. 4 rides at $1.50 plus 8 rides at $0.50
11. 3 rides at $1.50 plus 5 rides at $1 plus 1 ride at $0.50
12. 3 rides at $1.50 plus 4 rides at $1 plus 3 rides at $0.50
13. 3 rides at $1.50 plus 3 rides at $1 plus 5 rides at $0.50
14. 3 rides at $1.50 plus 2 rides at $1 plus 7 rides at $0.50
15. 3 rides at $1.50 plus 1 ride at $1 plus 9 rides at $0.50
16. 3 rides at $1.50 plus 11 rides at $0.50
17. 2 rides at $1.50 plus 7 rides at $1
18. 2 rides at $1.50 plus 6 rides at $1 plus 2 rides at $0.50
19. 2 rides at $1.50 plus 5 rides at $1 plus 4 rides at $0.50
20. 2 rides at $1.50 plus 4 rides at $1 plus 6 rides at $0.50
21. 2 rides at $1.50 plus 3 rides at $1 plus 8 rides at $0.50
22. 2 rides at $1.50 plus 2 rides at $1 plus 10 rides at $0.50
23. 2 rides at $1.50 plus 1 ride at $1 plus 12 rides at $0.50
24. 2 rides at $1.50 plus 14 rides at $0.50
25. 1 ride at $1.50 plus 8 rides at $1 plus 1 ride at $0.50
26. 1 ride at $1.50 plus 7 rides at $1 plus 3 rides at $0.50
27. 1 ride at $1.50 plus 6 rides at $1 plus 5 rides at $0.50
28. 1 ride at $1.50 plus 5 rides at $1 plus 7 rides at $0.50
29. 1 ride at $1.50 plus 4 rides at $1 plus 9 rides at $0.50
30. 1 ride at $1.50 plus 3 rides at $1 plus 11 rides at $0.50
31. 1 ride at $1.50 plus 2 rides at $1 plus 13 rides at $0.50
32. 1 ride at $1.50 plus 1 rides at $1 plus 15 rides at $0.50
33. 1 ride at $1.50 plus 17 rides at $0.50
34. 10 rides at $1
35. 9 rides at $1 plus 2 rides at $0.50
36. 8 rides at $1 plus 4 rides at $0.50
37. 7 rides at $1 plus 6 rides at $0.50
38. 6 rides at $1 plus 8 rides at $0.50
39. 5 rides at $1 plus 10 rides at $0.50
40. 4 rides at $1 plus 12 rides at $0.50
41. 3 rides at $1 plus 14 rides at $0.50
42. 2 rides at $1 plus 16 rides at $0.50
43. 1 ride at $1 plus 18 rides at $0.50
44. 20 rides at $0.50