Question

question
madelyn is a high school basketball player. in a particular game, she made some free throws (worth one point each) and some two point shots. madelyn made a total of 13 shots altogether and scored a total of 21 points. determine the number of free throws madelyn made and the number of two point shots she made.
answer attempt 1 out of 5
madelyn made free throws and two point shots.

Explanation:

Step1: Define Variables

Let \( x \) be the number of free throws (1 - point shots) and \( y \) be the number of two - point shots.
We know two equations from the problem:

1. The total number of shots: \( x + y=13\) (since the sum of free throws and two - point shots is 13).
2. The total number of points: \( x+2y = 21\) (because each free throw is 1 point and each two - point shot is 2 points, and the total points are 21).

Step2: Solve the System of Equations

From the first equation \( x + y=13\), we can express \( x \) in terms of \( y \) as \( x=13 - y\).
Substitute \( x = 13 - y\) into the second equation \( x + 2y=21\):

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Step3: Find the Value of \( x \)

Now that we know \( y = 8\), substitute \( y = 8\) into \( x=13 - y\):
\( x=13 - 8=5\)

Answer:

Madelyn made \( 5 \) free throws and \( 8 \) two - point shots.