SOLUTION: A student must have an average (the Mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon's grades on the first four tests

Question 1143455: A student must have an average (the Mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon's grades on the first four tests were 77%, 63%, 92%, and 78%. What range of grades on the fifth test would give him a B in the course?
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.

You need to solve this inequality


    80 <=  < 90.


I will do it step by step :


    5*80 <= 77 + 63 + 92 + 78 + x  < 5*90

    400  <= 310 + x < 450

    400 - 310 <= x < 450 - 310

    90 <= x < 140.


But the value of x is restricted from the above by 100 automatically (= by the definition (!) ), so the 


ANSWER is : the student must get any grade equal or greater than 90.

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Another closely related question, which left aside, is "what is the maximum mean grade the student can reach ?"

The answer is = = 92.

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