In an audition of 45 contestants, the average score was 46 points. Given that the average score of the girl contestants was 70 points and that of the boy contestants was 30 points, find the number of boy contestants who participated in the audition.
| |
Girl contestants |
Boy contestants |
Total |
| Number |
1 u |
45 - 1 u |
45 |
| Value |
70 |
30 |
|
| Total value |
70 u |
1350 - 30 u |
2070 |
Number of girl contestants = 1 u
Number of boy contestants = 45 - 1 u
Total score of the girl contestants
= 1 u x 70
= 70 u
Total score of the boy contestants
= 30 x (45 - 1 u)
= 1350 - 30 u
Total score of the contestants
= 70 u + 1350 - 30 u
= 70 u - 30 u + 1350
= 40 u + 1350
Total score of the contestants
= 45 x 46
= 2070
40 u + 1350 = 2070
40 u = 2070 - 1350
40 u = 720
1 u = 720 ÷ 40 = 18
Number of boy contestants
= 45 - 1 u
= 45 - 18
= 27
Answer(s): 27
