In an audition of 20 dancers, the average score was 64 points. Given that the average score of the boy dancers was 80 points and that of the girl dancers was 40 points, find the number of girl dancers who participated in the audition.
|
Boy dancers |
Girl dancers |
Total |
Number |
1 u |
20 - 1 u |
20 |
Value |
80 |
40 |
|
Total value |
80 u |
800 - 40 u |
1280 |
Number of boy dancers = 1 u
Number of girl dancers = 20 - 1 u
Total score of the boy dancers
= 1 u x 80
= 80 u
Total score of the girl dancers
= 40 x (20 - 1 u)
= 800 - 40 u
Total score of the dancers
= 80 u + 800 - 40 u
= 80 u - 40 u + 800
= 40 u + 800
Total score of the dancers
= 20 x 64
= 1280
40 u + 800 = 1280
40 u = 1280 - 800
40 u = 480
1 u = 480 ÷ 40 = 12
Number of girl dancers
= 20 - 1 u
= 20 - 12
= 8
Answer(s): 8