In an audition of 30 singers, the average score was 62 points. Given that the average score of the female singers was 70 points and that of the male singers was 50 points, find the number of male singers who participated in the audition.
| |
Female singers |
Male singers |
Total |
| Number |
1 u |
30 - 1 u |
30 |
| Value |
70 |
50 |
|
| Total value |
70 u |
1500 - 50 u |
1860 |
Number of female singers = 1 u
Number of male singers = 30 - 1 u
Total score of the female singers
= 1 u x 70
= 70 u
Total score of the male singers
= 50 x (30 - 1 u)
= 1500 - 50 u
Total score of the singers
= 70 u + 1500 - 50 u
= 70 u - 50 u + 1500
= 20 u + 1500
Total score of the singers
= 30 x 62
= 1860
20 u + 1500 = 1860
20 u = 1860 - 1500
20 u = 360
1 u = 360 ÷ 20 = 18
Number of male singers
= 30 - 1 u
= 30 - 18
= 12
Answer(s): 12
