In September, the ratio of boys and girls in a school's Band was 4 : 7. In October, 77 new members joined the club. As a result, the ratio of boys to girls in the club became 6 : 5. There were 8 boys in the Band in September. How many of the new members were girls?
| |
Boys |
Girls |
| Before |
4 u |
7 u |
| Change |
+ 77 |
| After |
6 p |
5 p |
Number of boys at first = 4 u
4 u = 8
1 u = 8 ÷ 4 = 2
Total number of members at first
= 4 u + 7 u
= 11 u
= 11 x 2
= 22
Total number of members in the end
= 22 + 77
= 99
Total number of members in the end
= 6 p + 5 p
= 11 p
11 p = 99
1 p = 99 ÷ 11 = 9
Number of girls in the end
= 5 p
= 5 x 9
= 45
Number of girls at first
= 7 u
= 7 x 2
= 14
Number of new members who were girls
= 45 - 14
= 31
Answer(s): 31
