Question

Gavin is a highschool basketball player. In a particular game, he made some free throws and some three point shots. Gavin made a total of 13 shots altogether and scored a total of 25 points. Determine the number of free throws Gavin made and the number of three point shots he made.

Answer 1

Let \( x \) be the number of free throws that Gavin made, and let \( y \) be the number of three point shots he made. We have the following information:

1. Gavin made a total of 13 shots:
\[
x + y = 13
\]

2. The points from free throws (each worth 1 point) and three point shots (each worth 3 points) add up to 25 points:
\[
x + 3y = 25
\]

Now we have a system of two equations:
1. \( x + y = 13 \)
2. \( x + 3y = 25 \)

We can start by solving for \( x \) in terms of \( y \) using the first equation:
\[
x = 13 - y
\]

Next, we substitute \( x \) into the second equation:
\[
(13 - y) + 3y = 25
\]

Now, simplify and solve for \( y \):
\[
13 - y + 3y = 25
\]
\[
13 + 2y = 25
\]
\[
2y = 25 - 13
\]
\[
2y = 12
\]
\[
y = 6
\]

Now that we have \( y \), we can find \( x \):
\[
x = 13 - y = 13 - 6 = 7
\]

So, the number of free throws Gavin made is \( x = 7 \) and the number of three point shots he made is \( y = 6 \).

**Final Answer: Gavin made 7 free throws and 6 three point shots.**