Question

A basketball player scored 9 times during one game. She scored a total of 12 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws? She made two-point shots (Simplify your answer)

Answer 1

For the points scored during the game, let the two point shots be represented by a, and let the free throws be represented by b.

This means her total 12 points can be broken down into the following;

`\begin{gathered} a+b=9---(1) \\ 2a+b=12---(2) \end{gathered}`

Equation (1) means that all shots either two-pointers or free throws were a total of 9 (that is she scored 9 times). Equation (2) means that every two-pointer counted as 2, while every free throw counted as 1, and adding all points gave her 12 point in all. Therefore;

`\begin{gathered} a+b=9 \\ 2a+b=12 \\ \text{Let a = 9-b in equation }(1) \\ \text{Substitute for the value of a into equation (2)} \\ 2(9-b)+b=12 \\ \text{Expand the parenthesis} \\ 18-2b+b=12 \\ \text{Collect like terms} \\ 18-12=2b-b \\ 6=b \\ \text{Substitute for the value of b into equation (1)} \\ a+6=9 \\ \text{Subtract 6 from both sides} \\ a=3 \end{gathered}`

This means she scored 3 two point shots, and

She also scored 6 free throws