First step is to find what should be the required total of sum of Score after fourth test, to identify how much more or less she need to score in his fourth test.

Since Mean = (Sum of Scores)/number of test

using above formula we determine what is the required sum of score.

82 = (Sum of Scores)/4

⇒ 82 × 4 = 328

So in four test she should have score total as 328

So Score require in fourth test = Required Score Total - (total score in 3 tests)

= 328 - ( 72 + 97 + 82 ) = 77

So she need score of 77 to be at mean of 82 after fourth test and get qualify for the team