Question

gabriella is a high school basketball player. in a particular game, she made some two point shots and some three point shots. gabriella scored a total of 32 points and made 4 more three point shots than two point shots. determine the number of two point shots gabriella made and the number of three point shots she made.

answer attempt 1 out of 2

gabriella made \\(\square\\) two point shots and \\(\square\\) three point shots.

Explanation:

Step1: Define Variables

Let \( x \) be the number of two - point shots. Then the number of three - point shots is \( x + 4 \) (since she made 4 more three - point shots than two - point shots).

Step2: Set Up Equation for Points

The total points from two - point shots is \( 2x \) (because each two - point shot is worth 2 points) and the total points from three - point shots is \( 3(x + 4) \) (because each three - point shot is worth 3 points). The total number of points is 32. So we can set up the equation:

$$ 2x+3(x + 4)=32 $$

Step3: Solve the Equation

First, expand the left - hand side of the equation:

$$ 2x+3x+12 = 32 $$

Combine like terms:

$$ 5x+12=32 $$

Subtract 12 from both sides:

$$ 5x=32 - 12 $$

$$ 5x=20 $$

Divide both sides by 5:

$$ x=\frac{20}{5}=4 $$

Step4: Find the Number of Three - Point Shots

The number of three - point shots is \( x + 4 \). Substitute \( x = 4 \) into this expression:
\( x+4=4 + 4=8 \)

Answer:

Gabriella made 4 two point shots and 8 three point shots.