Sorry, 44 will only pull the 77.6 grade down to 70.88, so 44
is not the worst you can make and still end up with a 70. 
Since the exam counts 20%, the average of 77.6 counts 80%
So the equation is:
(.80)(77.6) + (.20)x = 70
  62.08 + .2x = 70
          .2x = 70 - 62.08
          .2x = 7.92
            x = 39.6
That's the worst you can do on the final exam.  [But if you can make
an 89.6 you can pull your grade up to 80.]
Edwin