In the first four examinations each of 100 marks, Mohan got 94, 73, 72

1.	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» 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.

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»

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.