In an audition of 30 contestants, the average score was 56 points. Given that the average score of the female contestants was 70 points and that of the male contestants was 50 points, find the number of male contestants who participated in the audition.
| |
Female contestants |
Male contestants |
Total |
| Number |
1 u |
30 - 1 u |
30 |
| Value |
70 |
50 |
|
| Total value |
70 u |
1500 - 50 u |
1680 |
Number of female contestants = 1 u
Number of male contestants = 30 - 1 u
Total score of the female contestants
= 1 u x 70
= 70 u
Total score of the male contestants
= 50 x (30 - 1 u)
= 1500 - 50 u
Total score of the contestants
= 70 u + 1500 - 50 u
= 70 u - 50 u + 1500
= 20 u + 1500
Total score of the contestants
= 30 x 56
= 1680
20 u + 1500 = 1680
20 u = 1680 - 1500
20 u = 180
1 u = 180 ÷ 20 = 9
Number of male contestants
= 30 - 1 u
= 30 - 9
= 21
Answer(s): 21
