Let x = the number of earrings she buys,
and y = the number of necklasses she buys:
Then
To make things easier divide that through by 12:
We also cannot have a negative number of either, so we
actually have this system:
The three boundary lines are the equations made by replacing
the inequality symbols by equal signs:
Get the intercept points on the line whose equation is
,
(0,6), (12,0)
The line whose equation is 
is the y-axis.
and the line whose equation is 
is the x-axis.
Plot those intercepts and draw the boundary lines:
So every point inside that triangle or on the boundary of
that triangle which ia a corner point of one of those little
squares in the grid represents a possible solution. There
are 49 such points and thus 49 different possible solutions,
They are given below. Note that the first case is the origin, (0,0),
which represent the case of not buying any earrings or any necklasses!!
1. The point (0,0) represents buying 0 earrings and 0 necklasses costs $0
2. The point (0,1) represents buying 0 earrings and 1 necklass costs $24
3. The point (0,2) represents buying 0 earrings and 2 necklasses costs $48
4. The point (0,3) represents buying 0 earrings and 3 necklasses costs $72
5. The point (0,4) represents buying 0 earrings and 4 necklasses costs $96
6. The point (0,5) represents buying 0 earrings and 5 necklasses costs $120
7. The point (0,6) represents buying 0 earrings and 6 necklasses costs $144
8. The point (1,0) represents buying 1 earrings and 0 necklasses costs $12
9. The point (1,1) represents buying 1 earrings and 1 necklass costs $36
10. The point (1,2) represents buying 1 earrings and 2 necklasses costs $60
11. The point (1,3) represents buying 1 earrings and 3 necklasses costs $84
12. The point (1,4) represents buying 1 earrings and 4 necklasses costs $108
13. The point (1,5) represents buying 1 earrings and 5 necklasses costs $132
14. The point (2,0) represents buying 2 earrings and 0 necklasses costs $24
15. The point (2,1) represents buying 2 earrings and 1 necklass costs $48
16. The point (2,2) represents buying 2 earrings and 2 necklasses costs $72
17. The point (2,3) represents buying 2 earrings and 3 necklasses costs $96
18. The point (2,4) represents buying 2 earrings and 4 necklasses costs $120
19. The point (2,5) represents buying 2 earrings and 5 necklasses costs $144
20. The point (3,0) represents buying 3 earrings and 0 necklasses costs $36
21. The point (3,1) represents buying 3 earrings and 1 necklass costs $60
22. The point (3,2) represents buying 3 earrings and 2 necklasses costs $84
23. The point (3,3) represents buying 3 earrings and 3 necklasses costs $108
24. The point (3,4) represents buying 3 earrings and 4 necklasses costs $132
25. The point (4,0) represents buying 4 earrings and 0 necklasses costs $48
26. The point (4,1) represents buying 4 earrings and 1 necklass costs $72
27. The point (4,2) represents buying 4 earrings and 2 necklasses costs $96
28. The point (4,3) represents buying 4 earrings and 3 necklasses costs $120
29. The point (4,4) represents buying 4 earrings and 4 necklasses costs $144
30. The point (5,0) represents buying 5 earrings and 0 necklasses costs $60
31. The point (5,1) represents buying 5 earrings and 1 necklass costs $84
32. The point (5,2) represents buying 5 earrings and 2 necklasses costs $108
33. The point (5,3) represents buying 5 earrings and 3 necklasses costs $132
34. The point (6,0) represents buying 6 earrings and 0 necklasses costs $72
35. The point (6,1) represents buying 6 earrings and 1 necklass costs $96
36. The point (6,2) represents buying 6 earrings and 2 necklasses costs $120
37. The point (6,3) represents buying 6 earrings and 3 necklasses costs $144
38. The point (7,0) represents buying 7 earrings and 0 necklasses costs $84
39. The point (7,1) represents buying 7 earrings and 1 necklass costs $108
40. The point (7,2) represents buying 7 earrings and 2 necklasses costs $132
41. The point (8,0) represents buying 8 earrings and 0 necklasses costs $96
42. The point (8,1) represents buying 8 earrings and 1 necklass costs $120
43. The point (8,2) represents buying 8 earrings and 2 necklasses costs $144
44. The point (9,0) represents buying 9 earrings and 0 necklasses costs $108
45. The point (9,1) represents buying 9 earrings and 1 necklass costs $132
46. The point (10,0) represents buying 10 earrings and 0 necklasses costs $120
47. The point (10,1) represents buying 10 earrings and 1 necklass costs $144
48. The point (11,0) represents buying 11 earrings and 0 necklasses costs $132
49. The point (12,0) represents buying 12 earrings and 0 necklasses costs $144
Edwin
