In an audition of 40 performers, the average score was 60 points. Given that the average score of the girl performers was 80 points and that of the boy performers was 40 points, find the number of boy performers who participated in the audition.
| |
Girl performers |
Boy performers |
Total |
| Number |
1 u |
40 - 1 u |
40 |
| Value |
80 |
40 |
|
| Total value |
80 u |
1600 - 40 u |
2400 |
Number of girl performers = 1 u
Number of boy performers = 40 - 1 u
Total score of the girl performers
= 1 u x 80
= 80 u
Total score of the boy performers
= 40 x (40 - 1 u)
= 1600 - 40 u
Total score of the performers
= 80 u + 1600 - 40 u
= 80 u - 40 u + 1600
= 40 u + 1600
Total score of the performers
= 40 x 60
= 2400
40 u + 1600 = 2400
40 u = 2400 - 1600
40 u = 800
1 u = 800 ÷ 40 = 20
Number of boy performers
= 40 - 1 u
= 40 - 20
= 20
Answer(s): 20
