In an audition of 25 contestants, the average score was 56 points. Given that the average score of the boy contestants was 60 points and that of the girl contestants was 50 points, find the number of girl contestants who participated in the audition.
| |
Boy contestants |
Girl contestants |
Total |
| Number |
1 u |
25 - 1 u |
25 |
| Value |
60 |
50 |
|
| Total value |
60 u |
1250 - 50 u |
1400 |
Number of boy contestants = 1 u
Number of girl contestants = 25 - 1 u
Total score of the boy contestants
= 1 u x 60
= 60 u
Total score of the girl contestants
= 50 x (25 - 1 u)
= 1250 - 50 u
Total score of the contestants
= 60 u + 1250 - 50 u
= 60 u - 50 u + 1250
= 10 u + 1250
Total score of the contestants
= 25 x 56
= 1400
10 u + 1250 = 1400
10 u = 1400 - 1250
10 u = 150
1 u = 150 ÷ 10 = 15
Number of girl contestants
= 25 - 1 u
= 25 - 15
= 10
Answer(s): 10
