Question

Find two positive numbers if their ratio is 8:5 and the difference is 150.

Answer 1

a, b - the numbers

`\left\{\begin{array}{ccc}(a)/(b)=(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`
Answer: 400 and 250.