Linear Inequations-23

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In the first four papers each of 100 marks, Richard got 95, 72, 73, 83 marks.
If he wants an average of greater than or equal to 75 marks and less than 80 marks,
find the range of marks he should score in the fifth paper.

Solution: Suppose Richard scores x in the fifth paper. Then,

75 ≤ (95 + 72 + 73 + 83 + x)/5 < 80

=>75 ≤ (323 + x)/5 < 80

=> 375 < (323 + x) < 400

=> 52 < x < 77

Hence, Richard must score between 52 and 77 marks.

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