Nathan is a high school basketball player. In a particular game, he made some three point shots and some two point shots. Nathan scored a total of 22 points and made 4 times as many two point shots as three point shots. Determine the number of three point shots Nathan made and the number of two point shots he made.
Let:
x = number of three point shots
y = number of two point shots
From the given information, we can set up the following equations:
1. x + y = total number of shots
2. 3x + 2y = total points
We are given that Nathan scored a total of 22 points, so we can substitute this into equation 2:
1. x + y = 22
2. 3x + 2y = 22
It is also given that Nathan made 4 times as many two point shots as three point shots, so we can write:
y = 4x
Now we can substitute y = 4x into equation 1 and solve for x:
x + 4x = 22
5x = 22
x = 22/5
x = 4.4
Since you can't have a fraction of a shot, we know that Nathan must have made 4 three point shots.
Now we substitute x = 4 into y = 4x to find y:
y = 4*4
y = 16
So, Nathan made 4 three point shots and 16 two point shots.