student-name

Joyce Huang asked in Math

The average test score of a class was 71 marks. After four students who scored an average of 68 left the class, the average score of the remaining students became 73 marks. How many students were there in the class at first?

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student-name

Varun Rawat answered this

Let the original number of students in the class = nLet x be the sum of the marks obtained by n studentsAverage marks of n students = 71sum of the marks obtained by n studentsno. of students = 71xn = 71n = 71x      .....1When 4 students left the class, then number of students become n - 4.Now, average marks of these 4 students = 68sum of the marks obtained by 4 students4 = 68sum of the marks obtained by 4 students = 272When 4 students left the class, then average marks of the class is 73.Now, 73 = sum of the marks obtained by n students - sum of the marks obtained by 4 studentsn - 473n - 292 = x - 27273 ×x71 - 292 = x - 272            Using 173 ×x71 - x = 292 - 2722x71 = 20x = 710Now, from 1, we getn = 71071 = 10So, number of students in the class = 10