[tex]\it x:y=3 \Rightarrow \dfrac{x}{y}=\dfrac{3}{1} \Rightarrow y=\dfrac{x}{3}\ \ \ \ \ (1)\\ \\ \\ x:z=6 \Rightarrow \dfrac{x}{z}=\dfrac{6}{1} \Rightarrow z=\dfrac{x}{6}\ \ \ \ \ (2)\\ \\ \\ x+y+z=100\ \stackrel{(1),(2)}{\Longrightarrow}\ x+\dfrac{x}{3}+\dfrac{x}{6}=100|_{\cdot6} \Rightarrow 6x+2x+x=600 \Rightarrow\\ \\ \\ \Rightarrow 9x=600 \Rightarrow x=\dfrac{600^{(3}}{9} \Rightarrow x=\dfrac{200}{3}[/tex]
