Answer
$x=100,$
$y=210,$
$z=190$
Work Step by Step
$\begin{cases}x+y+z=500\\
150x+135y+110z=64250\\
75x+135y+110z=56750
\end{cases}$
Multiplying the third equation by $-1$ and adding it to the first equation.
$\begin{cases}150x+135y+110z=64250\\
-75x-135y-110z=-56750\\
-- -- -- -- -- --\\
75x=7500
\end{cases}$
$x=100$.
Replacing the $x$ in equations and multiplying the first equation by $-110$ and adding it to the second equation.
$\begin{cases}-110y-110z=-44000\\
135y+110z=49250\\
-- -- -- --\\
25y=5250\end{cases}$
$y=210,$
$z=190$
