In an audition of 50 dancers, the average score was 58 points. Given that the average score of the boy dancers was 80 points and that of the girl dancers was 30 points, find the number of girl dancers who participated in the audition.
| |
Boy dancers |
Girl dancers |
Total |
| Number |
1 u |
50 - 1 u |
50 |
| Value |
80 |
30 |
|
| Total value |
80 u |
1500 - 30 u |
2900 |
Number of boy dancers = 1 u
Number of girl dancers = 50 - 1 u
Total score of the boy dancers
= 1 u x 80
= 80 u
Total score of the girl dancers
= 30 x (50 - 1 u)
= 1500 - 30 u
Total score of the dancers
= 80 u + 1500 - 30 u
= 80 u - 30 u + 1500
= 50 u + 1500
Total score of the dancers
= 50 x 58
= 2900
50 u + 1500 = 2900
50 u = 2900 - 1500
50 u = 1400
1 u = 1400 ÷ 50 = 28
Number of girl dancers
= 50 - 1 u
= 50 - 28
= 22
Answer(s): 22
