Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 36

A university employs a total of 600 teaching assistants and research assistants. There are three times as many teaching assistants as research assistants. Find the number of research assistants employed by the university.

If we let $x$ and $y$ be the number of teaching and research assistants respectively, then we have

$x+y = 600 \qquad$ Equation 1

And,

$x = 3y \qquad$ Equation 2

By substituting equation 2 to equation 1, we get


$
\begin{equation}
\begin{aligned}

3y+y =& 600
\\
4y =& 600
\\
y =& 150

\end{aligned}
\end{equation}
$


Then, by applying back substitution, we get


$
\begin{equation}
\begin{aligned}

x =& 3y
\\
=& 3(150)
\\
=& 450

\end{aligned}
\end{equation}
$



Therefore, the number of teaching assistant is 450 while the number of research assistant is 150.