a, b - the numbers
[tex]\left\{\begin{array}{ccc}\dfrac{a}{b}=\dfrac{8}{5}&|\text{cross multiply}\\a-b=150&|+b\end{array}\right\\ \left\{\begin{array}{ccc}5a=8b\\a=150+b\end{array}\right\\\\\text{substitute a=150+b to the first equation}\\\\5(150+b)=8b\\750+5b=8b\ \ \ \ |-5b\\3b=750\ \ \ \ |:3\\b=250\\\\a=150+b\to a=150+250=400[/tex]
Answer: 400 and 250.
