The average test score of a group of students was 83 marks. After three students who scored an average of 97 marks left the group, the average score of the group became 80 marks. How many students were there at first?
| |
At first |
Left |
In the end |
| Number |
1 u + 3 |
3 |
1 u |
| Value |
83 |
97 |
80 |
| Total value |
83 u + 249 |
291 |
80 u |
Number of students in the end = 1 u
Number of students at first = 1 u + 3
Total test score in the end
= 1 u x 80
= 80 u
Total test score at first
= 83(1 u + 3)
= 83 u + 249
Total test score for students who left
= 3 x 97
= 291
Total test score at first is equal to sum of the total score in the end and total score of the students who left.
83 u + 249 = 80 u + 291
83 u - 80 u = 291 - 249
3 u = 42
1 u = 42 ÷ 3 = 14
Number of students at first
= 1 u + 3
= 14 + 3
= 17
Answer(s): 17
