what is the minimum score on the third exam that will give an A? What about a B (between 80% and 90%)?

Question

In certain Algebra class there is a total of 200 possible points.  These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 50 points each.  A student has received homework scores of 7, 5, 10, 4, and 9 and the first two exam scores are 33 and 41.  Assuming that grades are assigned according to the standard scale and there are no weights assigned to any of the grades is it possible for the student to receive an A (90% and above) in the class and if so what is the minimum score on the third exam that will give an A?  What about a B (between 80% and 90%)?

Answer 1

Total score obtained = 7+5+10+4+9 = 35

Total points in B and C = 33 +41 = 74

Condition, (35 + 74 +A)/4 >= 90% of 50

or 109+A >= 45*4

or A>= 71

So the student should secure atleast 71 marks to obtain A, which is not possible.

Similarly, the condition to secure B is

(35 + 74 +A)/4 >= 80% of 50

or 109+A >= 40*4

or A>= 51

So in order to obtain grade B, the student should bring atleast 51 marks, which again is not possible.