[tex]x+y+z=4\ 130 \\ \frac{x+y+z}{x}=6, \ rest \ 50 \\ y-300=\frac{z}{6}\\ z+300=4y \\ y=\frac{z}{6}+300 \\ z+300=4(\frac{z}{6}+300)=\frac{4z}{6}+4 \cdot 300=\frac{2z}{3}+1 \ 200 \\ z=\frac{2z}{3}+900 \\ \frac{3z}{3}-\frac{2z}{3}=900 \ \Leftrightarrow \ \frac{z}{3}=900 \ \Leftrightarrow \ z=3 \cdot 900 \\ \Rightarrow \boxed{z=2 \ 700}; \\ y=\frac{2 \ 700}{6}+300=450+300 \\ \Rightarrow \boxed{y=750}; \\ x=4 \ 130-(2 \ 700+750)=4 \ 130-3 \ 450 \\ \Rightarrow \boxed{x=680}.[/tex]
