Question 519932
Let 
Socre of fifth exam = x

Avarage for five exams = (97+71+89+73+x)/5 = (324+x)/5
His exam average must be greater than or equal to 80 and less than 90

80&#8804;(324+x)/5<90

Now
For 80&#8804;(324+x)/5
80&#8804;(324+x)/5
Multiply by 5 
5*80&#8804;5*(324+x)/5
400&#8804;(324+x)
400-324&#8804;x
76&#8804;x

For
(324+x)/5<90
Multiply by 5 
5*(324+x)/5<90*5
324+x<450
x<450-324
x<126

Range of x 
76&#8804;x<126

Range of marks is between 76 and 125

He must score marks between 76 and 125 in his fifth test to maintain an average which will give him a grade B.

If the total marks of an exam is 100 then range must be between 76 and 100.