In an audition of 30 dancers, the average score was 46 points. Given that the average score of the female dancers was 70 points and that of the male dancers was 40 points, find the number of male dancers who participated in the audition.
| |
Female dancers |
Male dancers |
Total |
| Number |
1 u |
30 - 1 u |
30 |
| Value |
70 |
40 |
|
| Total value |
70 u |
1200 - 40 u |
1380 |
Number of female dancers = 1 u
Number of male dancers = 30 - 1 u
Total score of the female dancers
= 1 u x 70
= 70 u
Total score of the male 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 46
= 1380
30 u + 1200 = 1380
30 u = 1380 - 1200
30 u = 180
1 u = 180 ÷ 30 = 6
Number of male dancers
= 30 - 1 u
= 30 - 6
= 24
Answer(s): 24
