[tex]\it 27)\ x+2y+3z=200\ \ \ \ \ \ (1)\\ \\ \\ \dfrac{x}{3}=\dfrac{^{2)}y}{\ 7}=\dfrac{^{3)}z}{\ 11}\ \Rightarrow\ \dfrac{x}{3}=\dfrac{2y}{14}=\dfrac{3z}{33}=\dfrac{x+2y+3z}{3+14+33}\ \stackrel{(1)}{=}\ \dfrac{200}{50}=4\ \ \ \ (2)[/tex]
[tex]\it (2) \Rightarrow \begin{cases}\it \dfrac{x}{3}=4\ \Rightarrow\ x=3\cdot4\ \Rightarrow\ x=12\\ \\ \\ \it \dfrac{2y}{14}=4 \Rightarrow 2y=14\cdot4|_{:2} \Rightarrow y=7\cdot4=28\\ \\ \\ \it \dfrac{3z}{33}=4 \Rightarrow 3z=33\cdot4|_{:3} \Rightarrow z=11\cdot4=44\end{cases}[/tex]
