In an audition of 30 musicians, the average score was 62 points. Given that the average score of the boy musicians was 70 points and that of the girl musicians was 50 points, find the number of girl musicians who participated in the audition.
| |
Boy musicians |
Girl musicians |
Total |
| Number |
1 u |
30 - 1 u |
30 |
| Value |
70 |
50 |
|
| Total value |
70 u |
1500 - 50 u |
1860 |
Number of boy musicians = 1 u
Number of girl musicians = 30 - 1 u
Total score of the boy musicians
= 1 u x 70
= 70 u
Total score of the girl musicians
= 50 x (30 - 1 u)
= 1500 - 50 u
Total score of the musicians
= 70 u + 1500 - 50 u
= 70 u - 50 u + 1500
= 20 u + 1500
Total score of the musicians
= 30 x 62
= 1860
20 u + 1500 = 1860
20 u = 1860 - 1500
20 u = 360
1 u = 360 ÷ 20 = 18
Number of girl musicians
= 30 - 1 u
= 30 - 18
= 12
Answer(s): 12
