[tex]x+y+z=22 \\ x=2y =3z \\ y=x:2 \\ z=x:3 \\ \frac{x}{1} + \frac{x}{2} + \frac{x}{3} =22 \\ \frac{6x}{6}+ \frac{3x}{6} + \frac{2x}{6} = \frac{11x}{6} =22 \\ 11x=22 \cdot 6 \\ 11x=132 \\ x= \frac{132}{11} \\ \boxed{x=12} \\ y=x:2=12:2 \\ \boxed{y=6} \\ z=x:3=12:3 \\ \boxed{z=4} [/tex]
