In August, the ratio of girls and boys in a school's Band was 5 : 8. In September, 84 new members joined the club. As a result, the ratio of girls to boys in the club became 6 : 5. There were 10 girls in the Band in August. How many of the new members were boys?
| |
Girls |
Boys |
| Before |
5 u |
8 u |
| Change |
+ 84 |
| After |
6 p |
5 p |
Number of girls at first = 5 u
5 u = 10
1 u = 10 ÷ 5 = 2
Total number of members at first
= 5 u + 8 u
= 13 u
= 13 x 2
= 26
Total number of members in the end
= 26 + 84
= 110
Total number of members in the end
= 6 p + 5 p
= 11 p
11 p = 110
1 p = 110 ÷ 11 = 10
Number of boys in the end
= 5 p
= 5 x 10
= 50
Number of boys at first
= 8 u
= 8 x 2
= 16
Number of new members who were boys
= 50 - 16
= 34
Answer(s): 34
