[tex]a+b+c=117 \\\\ a=2b \\\\ c : a=4 \ rest \ 7 \to c=4a+7 \ \textless \ =\ \textgreater \ c=4*2b+7 \to c=8b+7 \\\\\\ 2b+b+8b+7=117 \\\\ 11b=117-7 \\\\ 11b=110 \ \ \ |:11 \\\\ \boxed{b=10} \\\\ a=2b \\\\a=2*10 \\\\ \boxed{a=20} \\\\ c=8*10+7 \\\\ c=80+7 \\\\ \boxed{c=87}[/tex]