[tex]\{a,b\} i.p.\{4,5\}\Rightarrow \frac{a}{\frac{1}{4}}=\frac{b}{\frac{1}{5}}=k\Rightarrow a=\frac{k}{4},b=\frac{k}{5}\\
a+b=36\\
\frac{k}{4}+\frac{k}{5}=36|\cdot 20\\
5k+4k=720\\
9k=720\\
\boxed{k=80}\\
a=\frac{k}{4}\Rightarrow \boxed{a=20}\\
a=\frac{k}{5}\Rightarrow \boxed{b=16}[/tex]
