Question

Carol is playing basketball. When she shoots and scores a basket inside 15 feet

the shot is worth 2 points and when she shoots and scores a basket outside 15
feet the shot is worth 3 points. Carol earned 22 points during the game and took
a total of 10 shots. How many 3 point shots did she make?

Answer 1

By setting up a system of equations with x being the number of 2-point shots and y being the number of 3-point shots, we can determine that Carol made 2 three-point shots to score 22 points with 10 shots.

Step-by-step explanation:

Carol earned 22 points from 10 shots with a mix of 2-point and 3-point baskets. Let's define two variables: x is the number of 2-point shots she made, and y is the number of 3-point shots she made. We know that:

1. x + y = 10 (total shots made)
2. 2x + 3y = 22 (total points scored)

To find out how many 3-point shots Carol made (y), we need to solve this system of equations. Subtracting the first equation from the second (multiplied by 2) gives us:

2x + 3y = 22
- (2x + 2y = 20)
-----------------
y = 2

Carol made 2 three-point shots.