[tex]\it Fie\ a,\ b,\ c\ numerele\ cerute. \\ \\ a+b+c=150\ \ \ \ \ (1)\\ \\ \{a,\ b,\ c\}\ d.\ p.\ \{4,\ 5,\ 6\} \Rightarrow \dfrac{a}{4}= \dfrac{b}{5}= \dfrac{c}{6} = \dfrac{a+b+c}{4+5+6}\ \stackrel{(1)}{=}\ \dfrac{150}{15} =10\ \ \ \ \ \ (2)\\ \\ \\ (2)\ \Rightarrow\begin{cases}\it \dfrac{a}{4}=10\ \Rightarrow a=40\\ \\ \\ \it \dfrac{b}{5}=10 \Rightarrow b=50\\ \\ \\ \it \dfrac{c}{6}=10 \Rightarrow c=60. \end{cases}[/tex]
