In an audition of 40 performers, the average score was 55 points. Given that the average score of the boy performers was 70 points and that of the girl performers was 40 points, find the number of girl performers who participated in the audition.
| |
Boy performers |
Girl performers |
Total |
| Number |
1 u |
40 - 1 u |
40 |
| Value |
70 |
40 |
|
| Total value |
70 u |
1600 - 40 u |
2200 |
Number of boy performers = 1 u
Number of girl performers = 40 - 1 u
Total score of the boy performers
= 1 u x 70
= 70 u
Total score of the girl performers
= 40 x (40 - 1 u)
= 1600 - 40 u
Total score of the performers
= 70 u + 1600 - 40 u
= 70 u - 40 u + 1600
= 30 u + 1600
Total score of the performers
= 40 x 55
= 2200
30 u + 1600 = 2200
30 u = 2200 - 1600
30 u = 600
1 u = 600 ÷ 30 = 20
Number of girl performers
= 40 - 1 u
= 40 - 20
= 20
Answer(s): 20
