[tex]a)~ \frac{a}{2}= \frac{b}{6}= \frac{c}{7}= \frac{a+b+c}{2+6+7}= \frac{135}{15}=9. \\ \\ \frac{a}{2}=9 \Rightarrow a=18. \\ \\ \frac{b}{6}=9 \Rightarrow b=54. \\ \\ \frac{c}{7}=9 \Rightarrow c=63.[/tex]
[tex]b)~ \frac{a}{2}= \frac{b}{6}= \frac{c}{7}=k \Rightarrow a=2k;~b=6k;~c=7k. \\ \\ 3a+2b+5c=106 \\ 3 \cdot 2k+2 \cdot 6k+ 5 \cdot 7k=106 \\ 6k+12k+35k=106 \\ 53k=106 \Rightarrow k=2. \\ \\ a=2k = 2 \cdot 2=4. \\ b=6 k=6 \cdot 2=12. \\ c=7k=7 \cdot 2=14. [/tex]
