Question

In the first four examinations, each of 100 marks, Hamid got 94, 73, 72 and 84 marks. If a final average greater than or equal to 80 and less than 90 is needed to obtain a final grade B in a course, what range of marks in the fifth (last) examination will result in Hamid receiving ‘B’ in the course?

Answer 1

Let x be the mark on the fifth exam.

The average of the five exams is `(94+73+72+84+x)/5 = (323 + x)/5`

Require `80 ≤ (323 + x)/5 < 90`

Multiply by 5:

400 ≤ 323 + x < 450

So 77 ≤ x < 127

Since exam marks are between 0 and 100, the feasible range is

x ∈ [77, 100].