In an audition of 40 musicians, the average score was 52 points. Given that the average score of the boy musicians was 70 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 |
40 - 1 u |
40 |
| Value |
70 |
40 |
|
| Total value |
70 u |
1600 - 40 u |
2080 |
Number of boy musicians = 1 u
Number of girl musicians = 40 - 1 u
Total score of the boy musicians
= 1 u x 70
= 70 u
Total score of the girl musicians
= 40 x (40 - 1 u)
= 1600 - 40 u
Total score of the musicians
= 70 u + 1600 - 40 u
= 70 u - 40 u + 1600
= 30 u + 1600
Total score of the musicians
= 40 x 52
= 2080
30 u + 1600 = 2080
30 u = 2080 - 1600
30 u = 480
1 u = 480 ÷ 30 = 16
Number of girl musicians
= 40 - 1 u
= 40 - 16
= 24
Answer(s): 24
