Fie x, y, z cele trei părți.
x+y+z = 121 (1)
[tex]\it \{x,\ y,\ z\}\ d.\ p.\ \{2,\ 4,\ 5\} \Rightarrow \dfrac{x}{2}=\dfrac{y}{4}=\dfrac{z}{5}=\dfrac{x+y+z}{2+4+5}\ \stackrel{(1)}{=}\dfrac{121}{11}=11\ \ \ \ \ (2)\\ \\ \\ (2) \Rightarrow \begin{cases} \it \dfrac{x}{2}=11 \Rightarrow x=2\cdot11=22\\ \\ \it \dfrac{y}{4}=11 \Rightarrow y=4\cdot11=44\\ \\ \it \dfrac{z}{5}=11 \Rightarrow z=5\cdot11=55\end{cases}[/tex]
