Ive tried so many different ways using the formula for series capacitors and Q=CV and Ive had no luck solving this problem.

There must be some rule (or trick) Im missing involving combing C12 and C13 that im completely missing. Can anyone offer any insight into solving this problem?

you should be able to find [tex]C_1[/tex], [tex]C_2[/tex], and [tex]C_3[/tex] with these equations (they all depend on the voltage, but because the fourth eq. should use the same voltage, it cancels out...)