I know the title is confusing but that is because of 150-character limit, if anyone of you can improve it , please do.
Consider $\triangle ABC.$ Choose a point $D$ on segment $BC$ such that $BD/DC=1/2$.
Choose a point $E$ on segment $AC$ such that $AE/EC =2/3$ .
Let segments $AD$ and $BE$ intersect at point $P$.
If area of $\triangle PBD = 5$ sq. units, then ﬁnd the area of quadrilateral $PDCE$.
Here is a sketch that I drew:
Let $A(\triangle APB)=x$ , $A(\triangle APE)=y$ , $A$( quadrilateral $PDCE$)=$z$
$(x+5)/(y+z)=1/2$ , $(x+y)/(5+z)=2/3$.
$y = x/5+6, z = ((9 x)/5)+4$
But so what ? I want actually the numerical value of $z$ . What should I do now? Any hints are apreciated. (This is not class-homework , I'm solving sample questions for a competitive exam )