[tex]\it \{a,\ b,\ c\}\ d.\ p.\ \{3,\ 8,\ 10\} \Rightarrow a=3k,\ \ b=8k,\ \ c=10k\ \ \ \ \ \ (1)\\ \\ \{c,\ d,\ e\}\ i.\ p.\ \{4,\ 5,\ 9\} \Rightarrow 4c=5d=9e\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 4\cdot10k=5d=9e \Rightarrow d=8k, e=\dfrac{40}{9}k\ \ \ \ \ \ (3)[/tex]
[tex]\it a+b+c+d+e=903\ \stackrel{(1),(3)}{\Longrightarrow}\ 3k+8k+10K+8k+\dfrac{40}{9}k=903 \Rightarrow \\ \\ \\ \Rightarrow 29k+\dfrac{40}{9}k=903|_{\cdot9} \Rightarrow 261k+40k=9\cdot903 \Rightarrow 301k=9\cdot903|_{:301} \Rightarrow \\ \\ \\ \Rightarrow k=9\cdot3=27[/tex]
[tex]\it a=3k=3\cdot27=81\\ \\ b=8k=8\cdot27=216\\ \\ c+10k=10\cdot27=270\\ \\ d=8k=8\cdot27=216\\ \\ e=\dfrac{40}{9}\cdot27=40\cdot3=120[/tex]
