In an audition of 35 contestants, the average score was 52 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 |
35 - 1 u |
35 |
| Value |
60 |
50 |
|
| Total value |
60 u |
1750 - 50 u |
1820 |
Number of boy contestants = 1 u
Number of girl contestants = 35 - 1 u
Total score of the boy contestants
= 1 u x 60
= 60 u
Total score of the girl contestants
= 50 x (35 - 1 u)
= 1750 - 50 u
Total score of the contestants
= 60 u + 1750 - 50 u
= 60 u - 50 u + 1750
= 10 u + 1750
Total score of the contestants
= 35 x 52
= 1820
10 u + 1750 = 1820
10 u = 1820 - 1750
10 u = 70
1 u = 70 ÷ 10 = 7
Number of girl contestants
= 35 - 1 u
= 35 - 7
= 28
Answer(s): 28
