In an audition of 50 contestants, the average score was 54 points. Given that the average score of the girl contestants was 70 points and that of the boy contestants was 50 points, find the number of boy contestants who participated in the audition.
| |
Girl contestants |
Boy contestants |
Total |
| Number |
1 u |
50 - 1 u |
50 |
| Value |
70 |
50 |
|
| Total value |
70 u |
2500 - 50 u |
2700 |
Number of girl contestants = 1 u
Number of boy contestants = 50 - 1 u
Total score of the girl contestants
= 1 u x 70
= 70 u
Total score of the boy contestants
= 50 x (50 - 1 u)
= 2500 - 50 u
Total score of the contestants
= 70 u + 2500 - 50 u
= 70 u - 50 u + 2500
= 20 u + 2500
Total score of the contestants
= 50 x 54
= 2700
20 u + 2500 = 2700
20 u = 2700 - 2500
20 u = 200
1 u = 200 ÷ 20 = 10
Number of boy contestants
= 50 - 1 u
= 50 - 10
= 40
Answer(s): 40
