In an audition of 50 musicians, the average score was 43 points. Given that the average score of the boy musicians was 80 points and that of the girl musicians was 30 points, find the number of girl musicians who participated in the audition.
|
Boy musicians |
Girl musicians |
Total |
Number |
1 u |
50 - 1 u |
50 |
Value |
80 |
30 |
|
Total value |
80 u |
1500 - 30 u |
2150 |
Number of boy musicians = 1 u
Number of girl musicians = 50 - 1 u
Total score of the boy musicians
= 1 u x 80
= 80 u
Total score of the girl musicians
= 30 x (50 - 1 u)
= 1500 - 30 u
Total score of the musicians
= 80 u + 1500 - 30 u
= 80 u - 30 u + 1500
= 50 u + 1500
Total score of the musicians
= 50 x 43
= 2150
50 u + 1500 = 2150
50 u = 2150 - 1500
50 u = 650
1 u = 650 ÷ 50 = 13
Number of girl musicians
= 50 - 1 u
= 50 - 13
= 37
Answer(s): 37