Question

In the first four examinations each of 100 marks, Mohan 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, than what range of marks in the fifth (last) examination will result, if Mohan receiving grade B in the course?

Answer 1

Let x be the score obtained by Mohan in the last examination.

Then,

80 ≤ \(\frac{94+73+72+84+x}{5}\) < 90

⟹ 80 ≤ \(\frac{323+x}{5}\) < 90

⟹ 400 ≤ 323 + x < 450 

[Multiplying both sides by 5]

⟹ 400 − 323 ≤ 323 + x − 323 < 450 − 323

[Subtracting 3 from both sides]

⟹ 77 ≤ x > 127

Since, the upper limit is 100, 

therefore the required range is 77 ≤ x ≥ 100.