Argon $(\ce{Ar})$ and helium $(\ce{He})$ are initially in separate compartments of a container at $\pu{25 °C}.$ The $\ce{Ar}$ in compartment A which has a volume $V_\ce{A}$ of $\pu{9.00 L}$ and a pressure of $\pu{2.00 bar}.$ The $\ce{He}$ in compartment B of unknown volume $V_\ce{B}$ has a pressure of $\pu{6.00 bar}.$ When the two compartments are connected and the gases allowed to mix, the total pressure of gas is $\pu{3.60 bar}.$ Assume both gases behave ideally.
$$ \begin{array}{|l|l|} \hline \text{Chamber A} & \text{Chamber B} \\ V_\ce{A} = \pu{9.00 L} & V_\ce{B} = \pu{??? L} \\ p_\ce{A} = \pu{2.00 bar} & p_\ce{B} = \pu{6.00 bar} \\ \hline \end{array} $$
[4 marks] Determine the volume of compartment B.
I've been stuck on this problem for a while. Could someone walk me through the beginning steps? I should be good to go with some guidance. Would I use Boyle's law in attempt to find the final volume once the partition is removed?