Question

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.

Explanation:

Step1: Define Variables

Let \( x \) be the number of three - point shots and \( y \) be the number of two - point shots.

Step2: Set Up Equations

We know two things:

1. The total points scored: Each three - point shot is worth 3 points and each two - point shot is worth 2 points, and the total score is 22. So, \( 3x + 2y=22 \).
2. The relationship between the number of two - point and three - point shots: He made 4 times as many two - point shots as three - point shots, so \( y = 4x \).

Step3: Substitute and Solve

Substitute \( y = 4x \) into the first equation \( 3x+2y = 22 \).
We get \( 3x+2(4x)=22 \).
Simplify the left - hand side: \( 3x + 8x=22 \), which is \( 11x = 22 \).
Divide both sides by 11: \( x=\frac{22}{11}=2 \).

Step4: Find the Number of Two - Point Shots

Since \( y = 4x \) and \( x = 2 \), then \( y=4\times2 = 8 \).

Answer:

The number of three - point shots is 2 and the number of two - point shots is 8.