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