Question

Rachel Newton scored 31 points in a recent basketball game. She scored 21 times, making several free throws worth 1 point each and several field goals worth two points each. How many 2-point field goals did she make?

Answer 1

10

Explanation:

This problem can be solved with a system of equations...

Lets say that x is the number of free throws worth one point that Rachel made and that y is the number of two-point field goals that Rachel made.

We know that Rachel scored 21 times, so

x + y = 21.

We also know that Rachel scored 31 points, and each field goal made(y) is worth two points, so

x + 2y = 31

Now, to find the number of 2-point field goals she made, we need to solve the following system,

1)x + y = 21

2)x + 2y = 31

Our value of interest is y, so we can write x as function of y, from equation 1) and replacing it in equation 2)

So

x = 21 - y

Replacing in 2)

21 - y + 2y = 31

y = 31-21

y = 10

So, Rachel Newton made 10 2-point field goals.