Notăm cele patru numere cu a, b, c, d.
a < b < c < d.
2a > d cu 10 ⇒ 2a = d +1 0⇒ d = 2a - 10 (1)
[tex]\it \{a,\ b,\ c,\ d \}\ d.\ p.\ \{6,\ 8,\ 9,\ 11\} \Rightarrow \dfrac{a}{6}=\dfrac{b}{8}=\dfrac{c}{9}=\dfrac{d}{11}=k \Rightarrow \\ \\ \\ \Rightarrow \begin{cases} \it a=6k\\ \\ \it b=8k\\ \\ \it c=9k\\ \\ \it d=11k\end{cases}\ \ \ \ \ (2)\\ \\ \\ d=11k\ \stackrel{(1)}{\Longrightarrow}\ 2a-10=11k\ \ \ \ (3)[/tex]
[tex]\it Dar,\ a=6k|_{\cdot2} \Rightarrow 2a=12k\ \ \ \ (4)\\ \\ (3),\ (4) \Rightarrow 12k-10=11k \Rightarrow 12k-11k=10 \Rightarrow k=10\\ \\ \\ k=10\ \stackrel{(2)}{\Longrightarrow}\ \begin{cases} \it a=6\cdot10=60\\ \\ \it b=8\cdot10=80\\ \\ \it c=\9\cdot10=90\\ \\ \it d=11\cdot10=110\end{cases}[/tex]
