Answer
$$\overline x = \frac{9}{{11}}$$
Work Step by Step
$$\eqalign{
& {m_1} = 7,{\text{ }}{m_2} = 4,{\text{ }}{m_3} = 3,{\text{ }}{m_4} = 8 \cr
& {\text{Located at }} \cr
& {x_1} = - 3,{\text{ }}{x_2} = - 2,{\text{ }}{x_3} = 5,{\text{ }}{x_4} = 4 \cr
& {\text{The moment about the origin is }} \cr
& {M_0} = {m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3} + {m_4}{x_4} \cr
& {M_0} = \left( 7 \right)\left( { - 3} \right) + \left( 4 \right)\left( { - 2} \right) + \left( 3 \right)\left( 5 \right) + \left( 8 \right)\left( 4 \right) \cr
& {M_0} = 18 \cr
& m{\text{ is the total mass of the system}} \cr
& m = {m_1} + {m_2} + {m_3} + {m_4} \cr
& m = 7 + 4 + 3 + 8 \cr
& m = 22 \cr
& {\text{The center of mass is }}\overline x = \frac{{{M_0}}}{m}{\text{, then}} \cr
& \overline x = \frac{{18}}{{22}} \cr
& \overline x = \frac{9}{{11}} \cr} $$
