What should be a basic problem

Hello to All!

I am for some reason struggling with what should be very basic. This is part of a worked Thermo Dynamics problem and I have followed all logic to the final point where the final volume in a piston is to be found. In the attached screen shot you can see the numbers I am working with. However I have triend substituting in the gas law to the 1st law of thermo dynamics and have not been able to create an identity between the two sides and likewise can't follow the logic of "Tfinal can be eliminated to give Vfinal" any help, as always, really appreicated.

Cheers,

Andy