The average quiz score of a group of students was 65 marks. After 6 students who scored an average of 76 marks joined the group, the average score of all the students became 68 marks. How many students were there in the group at first?
| |
At first |
Joined |
In the end |
| Number |
1 u |
6 |
1 u + 6 |
| Value |
65 |
76 |
68 |
| Total value |
65 u |
456 |
68 u + 408 |
Number of students at first = 1 u
Number of students in the end = 1 u + 6
Total quiz score at first
= 1 u x 65
= 65 u
Total quiz score for students who joined
= 6 x 76
= 456
Total quiz score in the end
= 68(1 u + 6)
= 68 u + 408
Total quiz score in the end is equal to sum of the total score at first and total score of the students who joined.
68 u + 408 = 65 u + 456
68 u - 65 u = 456 - 408
3 u = 48
1 u = 48 ÷ 3 = 16
Number of students at first
= 1 u
= 16
Answer(s): 16
