To receive grade ‘A’ in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four papers, find the minimum marks that she must score in the last paper to get grade ‘A’ in the course.
Given that, there is total of five papers that Shikha has attended.
The score in the first four papers is 87, 95, 92 and 94.
To receive grade ‘A,’ the average marks in the five papers must be 90 or more.
Let marks in the fourth paper be x.
According to the question, we need to find minimum x for which the average of all five papers would be at least 90 marks.
Average marks in five papers ≥ 90 …(i)
Let us find the average marks in five papers. It is given by
Substituting this value of average in the inequality (i), we get
⇒ (368 + x) ≥ 90 × 5
⇒ (368 + x) ≥ 450
⇒ x ≥ 450 – 368
⇒ x ≥ 82
This inequality means that Shikha should score at least 82 marks in her fifth test to have an average of at least 90 marks.
So, the minimum marks to get an average of 90 marks is 82.
Thus, the minimum marks required in the fifth test is 82.