We will have the following:
[tex](3.0\operatorname{kg}\cdot9.8m/s^2)(0.7m)+(2.5\operatorname{kg}\cdot9.8m/s^2)(0.4m)=F_{m3}\cdot0.3m[/tex][tex]\Rightarrow20.58N\cdot m+9.8N\cdot m=F_{m3}\cdot0.3m\Rightarrow30.38N\cdot m=F_{m3\cdot0.3m}[/tex][tex]\Rightarrow F_{m3}=\frac{30.38N\cdot m}{0.3m}\Rightarrow F_{m3}=\frac{1519}{15}N[/tex][tex]\Rightarrow m_3=\frac{(\frac{1519}{15}N)}{9.8m/s^2}\Rightarrow m_3=\frac{31}{3}kg[/tex][tex]\Rightarrow m_3=10.3333333\ldots kg\Rightarrow m_3\approx10.33\operatorname{kg}[/tex]
So, m3 will be exactly 31/3 kg, that is approximately 10.33 kg.
