Sam plays basketball and last season he made 104 total shots, scoring 200 total points. If the number of two-point shots he made is two less than five times the number of three-point shots made, how many foul shots (one point) did he make?
The solution is

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

36

step-by-step explanation: