In an audition of 20 musicians, the average score was 54 points. Given that the average score of the boy musicians was 80 points and that of the girl musicians was 40 points, find the number of girl musicians who participated in the audition.
| |
Boy musicians |
Girl musicians |
Total |
| Number |
1 u |
20 - 1 u |
20 |
| Value |
80 |
40 |
|
| Total value |
80 u |
800 - 40 u |
1080 |
Number of boy musicians = 1 u
Number of girl musicians = 20 - 1 u
Total score of the boy musicians
= 1 u x 80
= 80 u
Total score of the girl musicians
= 40 x (20 - 1 u)
= 800 - 40 u
Total score of the musicians
= 80 u + 800 - 40 u
= 80 u - 40 u + 800
= 40 u + 800
Total score of the musicians
= 20 x 54
= 1080
40 u + 800 = 1080
40 u = 1080 - 800
40 u = 280
1 u = 280 ÷ 40 = 7
Number of girl musicians
= 20 - 1 u
= 20 - 7
= 13
Answer(s): 13
