[tex]\{x,y,z\} ip\{1,(3);6,(6);0,(4)\}\Rightarrow \frac{\frac{x}{1}}{\frac{4}{3}}=\frac{\frac{y}{1}}{\frac{20}{3}}=\frac{\frac{z}{1}}{\frac{4}{9}}\Rightarrow \\
\\
\Rightarrow \frac{x}{\frac{3}{4}}=\frac{y}{\frac{3}{20}}=\frac{z}{\frac{9}{4}}=k\Rightarrow x=\frac{3k}{4} ,y=\frac{3k}{20},z=\frac{9k}{4}\\
x+y+z=1134\\
\frac{3k}{4}+\frac{3k}{20}+\frac{9k}{4}=1134|\cdot 20\\
15k+3k+45k=22680\\
63k=22680\\
\boxed{\boxed{k=360}}\\
x=\frac{3k}{4}=\boxed{270}\\
y=\frac{3k}{20}=\boxed{54}\\
[/tex]
[tex]z=\frac{9k}{4}=\boxed{810}[/tex]