[tex]\{ a,b,c\} d.p.\{0,2 ;0,7;0,9\} \Rightarrow \frac{a}{\frac{1}{5}}=\frac{b}{\frac{7}{10}}=\frac{c}{\frac{9}{10}}=k\Rightarrow a=\frac{k}{5}, b=\frac{7k}{10},c=\frac{9k}{10}\\
2a+3b+5c=252\\
\frac{2k}{5}+\frac{21k}{10}+\frac{45k}{10}=252 |\cdot 10\\
4k+21k+45k=2520\\
70k=2520 \Rightarrow \boxed{k=36}\\
a=\frac{36}{5}\\
\\
b=\frac{7\cdot 36}{10}=\frac{252}{10}\\
\\
c=\frac{9\cdot 36}{10}=\frac{324}{10}
[/tex]