In an audition of 30 dancers, the average score was 51 points. Given that the average score of the girl dancers was 60 points and that of the boy dancers was 50 points, find the number of boy dancers who participated in the audition.
| |
Girl dancers |
Boy dancers |
Total |
| Number |
1 u |
30 - 1 u |
30 |
| Value |
60 |
50 |
|
| Total value |
60 u |
1500 - 50 u |
1530 |
Number of girl dancers = 1 u
Number of boy dancers = 30 - 1 u
Total score of the girl dancers
= 1 u x 60
= 60 u
Total score of the boy dancers
= 50 x (30 - 1 u)
= 1500 - 50 u
Total score of the dancers
= 60 u + 1500 - 50 u
= 60 u - 50 u + 1500
= 10 u + 1500
Total score of the dancers
= 30 x 51
= 1530
10 u + 1500 = 1530
10 u = 1530 - 1500
10 u = 30
1 u = 30 ÷ 10 = 3
Number of boy dancers
= 30 - 1 u
= 30 - 3
= 27
Answer(s): 27
