Question

marques is a high school basketball player. in a particular game, he made some three point shots and some free throws (worth one point each). marques made a total of 8 shots altogether and scored a total of 12 points. determine the number of three point shots marques made and the number of free throws he made. answer attempt 1 out of 2 marques made three point shots and free throws.

Explanation:

Step1: Define variables

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

1. The total number of shots: \( x + y=8\) (since the total number of shots is 8)
2. The total number of points: \( 3x + y = 12\) (since each three - point shot is worth 3 points and each free throw is worth 1 point, and the total points are 12)

Step2: Solve the system of equations

Subtract the first equation \( x + y=8\) from the second equation \( 3x + y=12\).
\((3x + y)-(x + y)=12 - 8\)
Expand the left - hand side: \(3x + y-x - y=4\)
Simplify: \(2x=4\)
Divide both sides by 2: \(x = 2\)

Step3: Find the value of \( y \)

Substitute \( x = 2\) into the first equation \( x + y=8\).
\(2+y=8\)
Subtract 2 from both sides: \(y=8 - 2=6\)

Answer:

Marques made 2 three - point shots and 6 free throws.