In an audition of 50 musicians, the average score was 57 points. Given that the average score of the female musicians was 60 points and that of the male musicians was 50 points, find the number of male musicians who participated in the audition.
| |
Female musicians |
Male musicians |
Total |
| Number |
1 u |
50 - 1 u |
50 |
| Value |
60 |
50 |
|
| Total value |
60 u |
2500 - 50 u |
2850 |
Number of female musicians = 1 u
Number of male musicians = 50 - 1 u
Total score of the female musicians
= 1 u x 60
= 60 u
Total score of the male musicians
= 50 x (50 - 1 u)
= 2500 - 50 u
Total score of the musicians
= 60 u + 2500 - 50 u
= 60 u - 50 u + 2500
= 10 u + 2500
Total score of the musicians
= 50 x 57
= 2850
10 u + 2500 = 2850
10 u = 2850 - 2500
10 u = 350
1 u = 350 ÷ 10 = 35
Number of male musicians
= 50 - 1 u
= 50 - 35
= 15
Answer(s): 15
