In an audition of 45 musicians, the average score was 50 points. Given that the average score of the male musicians was 80 points and that of the female musicians was 30 points, find the number of female musicians who participated in the audition.
| |
Male musicians |
Female musicians |
Total |
| Number |
1 u |
45 - 1 u |
45 |
| Value |
80 |
30 |
|
| Total value |
80 u |
1350 - 30 u |
2250 |
Number of male musicians = 1 u
Number of female musicians = 45 - 1 u
Total score of the male musicians
= 1 u x 80
= 80 u
Total score of the female musicians
= 30 x (45 - 1 u)
= 1350 - 30 u
Total score of the musicians
= 80 u + 1350 - 30 u
= 80 u - 30 u + 1350
= 50 u + 1350
Total score of the musicians
= 45 x 50
= 2250
50 u + 1350 = 2250
50 u = 2250 - 1350
50 u = 900
1 u = 900 ÷ 50 = 18
Number of female musicians
= 45 - 1 u
= 45 - 18
= 27
Answer(s): 27
