Help with complex power and power factor correction problem
Now, part (b) and (c) seem easy enough to answer given enough
  information but I cannot figure out whether I'm understanding (a)
  right.


The question reads to me as if part(a) applies before the correction so....

Try looking up power factor phasor diagrams: -



You have an apparent power (volt*amps or VA) of 150 and, you have an angle of 24 degrees. Just apply pythagoras to calculate real (active) power. As bonus you can even calculate reactive power.