In an audition of 50 dancers, the average score was 48 points. Given that the average score of the girl dancers was 60 points and that of the boy dancers was 30 points, find the number of boy dancers who participated in the audition.
| |
Girl dancers |
Boy dancers |
Total |
| Number |
1 u |
50 - 1 u |
50 |
| Value |
60 |
30 |
|
| Total value |
60 u |
1500 - 30 u |
2400 |
Number of girl dancers = 1 u
Number of boy dancers = 50 - 1 u
Total score of the girl dancers
= 1 u x 60
= 60 u
Total score of the boy dancers
= 30 x (50 - 1 u)
= 1500 - 30 u
Total score of the dancers
= 60 u + 1500 - 30 u
= 60 u - 30 u + 1500
= 30 u + 1500
Total score of the dancers
= 50 x 48
= 2400
30 u + 1500 = 2400
30 u = 2400 - 1500
30 u = 900
1 u = 900 ÷ 30 = 30
Number of boy dancers
= 50 - 1 u
= 50 - 30
= 20
Answer(s): 20
