In an audition of 20 musicians, the average score was 40 points. Given that the average score of the female musicians was 80 points and that of the male musicians was 30 points, find the number of male musicians who participated in the audition.
| |
Female musicians |
Male musicians |
Total |
| Number |
1 u |
20 - 1 u |
20 |
| Value |
80 |
30 |
|
| Total value |
80 u |
600 - 30 u |
800 |
Number of female musicians = 1 u
Number of male musicians = 20 - 1 u
Total score of the female musicians
= 1 u x 80
= 80 u
Total score of the male musicians
= 30 x (20 - 1 u)
= 600 - 30 u
Total score of the musicians
= 80 u + 600 - 30 u
= 80 u - 30 u + 600
= 50 u + 600
Total score of the musicians
= 20 x 40
= 800
50 u + 600 = 800
50 u = 800 - 600
50 u = 200
1 u = 200 ÷ 50 = 4
Number of male musicians
= 20 - 1 u
= 20 - 4
= 16
Answer(s): 16
