[tex]x+y=80 \\ z=\frac{x}{2}=\frac{y}{3} \\ x=2z \\ y=3z \\ 2z+3z=80 \\ 5z=80 \\ z=\frac{80}{5} \\ \boxed{z=varsta \ copilului=\bold{16 \ ani}} \\ x=2z=2 \cdot 16 \ ani \\ \boxed{x=varsta \ mamei=\bold{32 \ ani}} \\ y=3z=3 \cdot 16 \ ani \\ \boxed{y=varsta \ tatalui=\bold{48 \ ani}}[/tex]
