[tex]a+b+c=22 \\ a:b=3 \\ a:c=2 \\ b=a:3 \\ c=a:2 \\ a+a:3+a:2=22 \\ a+\frac{a}{3}+\frac{a}{2}=22 \\ \frac{6a}{6}+\frac{2a}{6}+\frac{3a}{6}=22 \\ \frac{11a}{6}=22 \\ 11a=22 \cdot 6 \\ 11a=132 \\ a=\frac{132}{11} \\ \boxed{\bold{a=12}} \\ b=a:3=12:3 \\ \boxed{\bold{b=4}} \\ c=a:2=12:2 \\ \boxed{\bold{c=6}}[/tex]
