In a mathematics club, the average score of 15 students in a weekly quiz is 72.4. After including the scores of 5 more students, the overall average becomes 74.6. If the scores of three of the new students are 76.2, 78.5, and 80.4, respectively, and the remaining two have equal scores, find the score of each of the remaining two students.
Show answer & explanation
Correct answer: D
Explanation
Given:
Average of 15 students = 72.4
Total number of students = 20
New average = 74.6
Marks of three students = 76.2, 78.5, 80.4
Total marks of the first 15 students = 15 × 72.4 = 1086
Total marks of the 20 students = 20 × 74.6 = 1492
Total marks of the 5 new students = 1492 − 1086 = 406
Marks of the three students = 76.2 + 78.5 + 80.4 = 235.1
Total marks of the remaining two students = 406 − 235.1 = 170.9
Marks of each student = 170.9 / 2 = 85.45