In an audition of 30 dancers, the average score was 48 points. Given that the average score of the male dancers was 70 points and that of the female dancers was 40 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 |
40 |
|
| Total value |
70 u |
1200 - 40 u |
1440 |
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
= 40 x (30 - 1 u)
= 1200 - 40 u
Total score of the dancers
= 70 u + 1200 - 40 u
= 70 u - 40 u + 1200
= 30 u + 1200
Total score of the dancers
= 30 x 48
= 1440
30 u + 1200 = 1440
30 u = 1440 - 1200
30 u = 240
1 u = 240 ÷ 30 = 8
Number of female dancers
= 30 - 1 u
= 30 - 8
= 22
Answer(s): 22
