The average quiz score of a group of students was 63 marks. After 3 students who scored an average of 75 marks joined the group, the average score of all the students became 66 marks. How many students were there in the group at first?
|
At first |
Joined |
In the end |
Number |
1 u |
3 |
1 u + 3 |
Value |
63 |
75 |
66 |
Total value |
63 u |
225 |
66 u + 198 |
Number of students at first = 1 u
Number of students in the end = 1 u + 3
Total quiz score at first
= 1 u x 63
= 63 u
Total quiz score for students who joined
= 3 x 75
= 225
Total quiz score in the end
= 66(1 u + 3)
= 66 u + 198
Total quiz score in the end is equal to sum of the total score at first and total score of the students who joined.
66 u + 198 = 63 u + 225
66 u - 63 u = 225 - 198
3 u = 27
1 u = 27 ÷ 3 = 9
Number of students at first
= 1 u
= 9
Answer(s): 9