Answer
The moment M of the system about the origin is
$$
\begin{aligned}
M&=\sum_{i=1}^{3} m_{i} x_{i} \\
&=154
\end{aligned}
$$
The center of mass of the system is
$$
\begin{aligned}
\overline{x} &=M / m\\
&=\frac{M}{ \sum_{i=1}^{3} m_{i}} \\
&=\frac{154}{47}\\
\end{aligned}
$$
Work Step by Step
The moment M of the system about the origin is
$$
\begin{aligned}
M&=\sum_{i=1}^{3} m_{i} x_{i} \\
&=m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3} \\
&=12 \cdot (-3)+15 \cdot (2)+20 \cdot (8) \\
&=154
\end{aligned}
$$
The center of mass of the system is
$$
\begin{aligned}
\overline{x} &=M / m\\
&=\frac{M}{ \sum_{i=1}^{3} m_{i}} \\
&=\frac{M}{ m_{1} +m_{2} +m_{3}} \\
&=\frac{M}{ 12 +15+20 } \\
&=\frac{154}{47}\\
\end{aligned}
$$
