A problem by Sherry Sarkar

In Triangle $ABC$ , $AB$ = 48 , $BC$ = 27 , $AC$ = 32. $D$ is on $AC$ such that $AD$ = 20 and $E$ is on $AB$ such that $AE$ = 18. The ratio of the area of triangle $ADE$ to the area of quadrilateral $BEDC$ can be expressed as $\frac{a}{b}$ .

What is $a + b$ ?