[tex]\{a,b\}i.p.\{0,2;0,5\}\Rightarrow \dfrac{a}{\frac{1}{0,2}}=\dfrac{b}{\frac{1}{0,5}}\Rightarrow \dfrac{a}{5}=\dfrac{b}{2}=k\Rightarrow a=5k,b=2k\\
4a+3b=78\\
4\cdot 5k+3\cdot 2k=78\\
20k+6k=78\\
26k=78\\
\boxed{k=3}\\
a=5k\Rightarrow \boxed{a=15}\\
b=2k\Rightarrow \boxed{b=6}[/tex]
