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