# 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.