In an audition of 30 dancers, the average score was 52 points. Given that the average score of the male dancers was 70 points and that of the female dancers was 50 points, find the number of female dancers who participated in the audition.
|
Male dancers |
Female dancers |
Total |
Number |
1 u |
30 - 1 u |
30 |
Value |
70 |
50 |
|
Total value |
70 u |
1500 - 50 u |
1560 |
Number of male dancers = 1 u
Number of female dancers = 30 - 1 u
Total score of the male dancers
= 1 u x 70
= 70 u
Total score of the female dancers
= 50 x (30 - 1 u)
= 1500 - 50 u
Total score of the dancers
= 70 u + 1500 - 50 u
= 70 u - 50 u + 1500
= 20 u + 1500
Total score of the dancers
= 30 x 52
= 1560
20 u + 1500 = 1560
20 u = 1560 - 1500
20 u = 60
1 u = 60 ÷ 20 = 3
Number of female dancers
= 30 - 1 u
= 30 - 3
= 27
Answer(s): 27