Problem

Source: 2018 Singapore Mathematical Olympiad Senior Q4

Tags: algebra, inequalities, High school olympiad, singapore



Let $a,b,c,d$ be positive integers such that $a+c=20$ and $\frac{a}{b}+\frac{c}{d}<1$. Find the maximum possible value of $\frac{a}{b}+\frac{c}{d}$.