How to find the correct equations for solving the following geometry question?

Question

I am trying to solve the following question.

My attempt is as follows.

\begin{cases} x+a+b = 30\\ y+z+c+d=30\\ x+y+z+a=30\\ b+c+d=30\\ x+z+b+c=40\\ y+a+d=20\\ x+y+z+a+b+c+d=60 \end{cases}

Now I am confused in how to get $x-y$.

Answer 1

Draw $EM$ parallel to $AB$ we know $EH:BH=EM:BF=EM:AF=2:3$

Therefore $S_{CEH}={2\over5}S_{CEB}={2\over5}\cdot 40=16$

Also since $I$ is centroid we have $CI:IF=2:1$ so $S_{AIF}={1\over3}S_{CAF}={1\over3}\cdot 30=10$

Therefore the area difference is $16-10=6$.