Question

In the Varsity vs. Faculty basketballgame at Crestwood Christian School, atotal of 141 points were scored. If thevarsity scored 5 more than three timesas many points as the faculty, howmany points did the faculty score?

Answer 1

So,

We know that the total of points scored were 141.

Let "x" be the points scored by the faculty.

Let "y" be the points scored by the varsity.

When we say "the varsity scored 5 more than three times as many points as the faculty", we could write the following expressions:

- First. We know that the total of points scored were 141, so,

`x+y=141`

- Second. The varsity scored 5 more than three times as many points as the faculty. So,

`y=5+3x`

What we're going to do now is to solve the system:

`\begin{gathered} x+y=141 \\ y=5+3x \end{gathered}`

This could look a little bit complicated but it is not. We're going to follow the steps below:

Step 1. We could re-write this system as:

`\begin{gathered} y=141-x \\ y=5+3x \end{gathered}`

Notice that we can equal both equations and find the value of x:

`\begin{gathered} y=y \\ 141-x=5+3x \\ 141-5=x+3x \\ 136=4x \\ x=(136)/(4)=34 \end{gathered}`

As "x" are the points scored by the faculty, therefore, the faculty scored 34 points.