Clay Thompson scored 38 points in one game. He made both 2pt shots and 3 pt. Shots. He scored a total of 16 times. How many 2 pt shots did he make and how many 3 pt shots did he make?
number of 2-pointers ---- x
number of 3-pointers ----- 16-x
2x + 3(16-x) = 38
solve for x
post it.
To find out how many 2-pt shots Clay Thompson made and how many 3-pt shots he made, we can use the information given in the problem.
Let's assume that Clay Thompson made x 2-pt shots and y 3-pt shots.
According to the problem, Clay Thompson made a total of 16 shots. Therefore, we can create the equation:
x + y = 16 (equation 1)
We also know that Clay Thompson scored a total of 38 points. Since a 2-point shot is worth 2 points, and a 3-point shot is worth 3 points, we can use this information to create another equation:
2x + 3y = 38 (equation 2)
Now we have a system of two equations (equation 1 and equation 2) that we can solve simultaneously to find the values of x and y.
To solve the system, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply equation 1 by 2:
2x + 2y = 32 (equation 3)
Now, subtract equation 3 from equation 2:
(2x + 3y) - (2x + 2y) = 38 - 32
The x terms cancel out, and we are left with:
y = 6
Now that we have the value of y, we can substitute it back into equation 1 to solve for x:
x + 6 = 16
Subtract 6 from both sides:
x = 10
Therefore, Clay Thompson made 10 2-pt shots and 6 3-pt shots in the game.