Q16. - Algebra 1

Question

Casey made 84 field goals during the basketball season for a total of 183 points. Each field goal was worth either 2 or 3 points. How many 2-point and 3-point field goals did Casey make during the season?

Step-by-Step Solution

Answer

Casey made 69 2-point and 15 3-point field goals.

Step 1. Write equation.

Let $x$ represents the 2-point field goals and $y$ represents the 3-point field goals, such that

$$\begin{gathered} x+y=84 \\ 2x+3y=183 \end{gathered}$$

Step 2. Multiplication.

Multiply $x+y=84$ by 2 and subtract it from $2x+3y=183$.

$$\begin{gathered} 2x+3y-2\left(x+y\right)=183-2\left(84\right) \\ 2x+3y-2x-2y=15 \\ y=15 \end{gathered}$$

 

Step 3. Substitution.

Substitute 15 for $y$ into $x+y=84$ and simplify to find $x$.

$$\begin{gathered} x+15=84 \\ x=69 \end{gathered}$$ 

Therefore, Casey made 69 2-point and 15 3-point field goals.