Question

question
andres is a high school basketball player. in a particular game, he made some two point shots and some free throws (worth one point each). andres made a total of 12 shots altogether and scored a total of 16 points. determine the number of two point shots andres made and the number of free throws he made.
answer attempt 1 out of 2
andres made
two point shots and
free throws.

Explanation:

Step1: Define variables

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

1. The total number of shots: \( x + y=12 \) (since the total number of shots made is 12)
2. The total number of points: \( 2x + y = 16 \) (because each two - point shot is worth 2 points and each free throw is worth 1 point, and the total points are 16)

Step2: Solve the system of equations

Subtract the first equation from the second equation:
\((2x + y)-(x + y)=16 - 12\)
Simplify the left - hand side: \(2x + y-x - y=x\)
Simplify the right - hand side: \(16 - 12 = 4\)
So, \(x = 4\)

Step3: Find the value of \( y \)

Substitute \( x = 4 \) into the first equation \(x + y=12\)
\(4 + y=12\)
Subtract 4 from both sides: \(y=12 - 4=8\)

Answer:

Andres made 4 two - point shots and 8 free throws.