Answer
The two masses are 104 and 46 kg
Work Step by Step
We are given M$_{1}$ + M$_{2}$ = 150 kg which means M$_{1}$ = 150 kg - M$_2$. We also have $\frac{GM_1M_2}{(0.20 m)^{2}}$ = 8.00 $\times$ 10$^{-6}$
M$_{1}$M$_{2}$ = $\frac{(8.00 \times 10^{-6}N)(0.20 m)^{2}}{6.67 \times 10^{-11} N m^{2}/kg^{2}}$ = 4798 kg$^{2}$
Thus, ${(150 kg - M_2)M_2 = 4798 kg^2}$ or ${M_2^2 - (150 kg}M_2 + (4798 kg^2) = 0$.
Solving this equation gives $M_2 = 103.75 kg and 46.25 kg$. So the two masses are 104 and 46 kg
