In a basketball game, Sam scored 34 pts, consisting only of 3 point shots and 2 point shots. He made a total of 15 shots. How many shots of each type did he make?
3x+2y=34
x+y = 15 so y = 15-x
3x +2(15-x) = 34
3x + 30 -2x = 34
x = 4
y = 11
To determine the number of shots of each type Sam made, we can set up a system of equations based on the given information.
Let's assume Sam made x 3-point shots and y 2-point shots.
From the given information, we can start with two equations:
1) The total number of shots Sam made is 15:
x + y = 15
2) The total number of points Sam scored is 34, where each 3-point shot is worth 3 points and each 2-point shot is worth 2 points:
3x + 2y = 34
To solve this system of equations, we can use the substitution method or the elimination method.
Let's solve it using the elimination method:
Multiply the first equation by 2:
2(x + y) = 2(15) -> 2x + 2y = 30
Now, subtract this equation from the second equation:
(3x + 2y) - (2x + 2y) = 34 - 30
This simplifies to:
3x - 2x = 4
x = 4
Substitute the x value into the first equation:
4 + y = 15
y = 15 - 4
y = 11
Therefore, Sam made 4 shots worth 3 points each and 11 shots worth 2 points each.