Answer: he made 22 foul shots
Step-by-step explanation:
Let x represent the number of one point shot that he made.
Let y represent the number of two point shots that he made.
Let z represent the number of three point shots that he made.
If the number of two-point shots he made is two less than five times the number of three-point shots made, it means that
y = 5z - 2
he made 104 total shots. It means that
x + y + z = 104- - - - - - - - - - 1
Substituting y = 5z - 2 into equation 1, it becomes
x + 5z - 2 + z = 104
x + 6z = 106- - - - - - - - - - -2
Total number of points scored is 200. It means that
x + 2y + 3z = 200- - - - - - - - - - 3
Substituting y = 5z - 2 into equation 3, it becomes
x + 2(5z - 2) + 3z = 200
x + 10z - 4 + 3z = 200
x + 13z = 204- - - - - - - - - - 4
Subtracting equation 4 from equation 2, it becomes
- 7z = - 98
z = - 98/ - 7
z = 14
Substituting z = 14 into equation 2, it becomes
x + 6 × 14 = 106
x + 84 = 106
x = 106 - 84
x = 22
