There were 9 more boys than girls in the gymnasium. Excluding 12 girls, the number of girls was
23 of the number of boys. When another 7 boys joined, what fraction of the pupils were boys in the end? Give your answer in its simplest form.
|
Boys |
Girls |
Comparing boys and girls at first |
9 more |
|
Before |
3 u |
2 u + 12 |
Change |
+ 7 |
|
After |
3 u + 7 |
2 u + 12 |
Number of boys at first was 9 more than the number of girls. If another 9 girls entered the gymnasium at first, the number of boys and girls at first would be the same.
3 u = 2 u + 12 + 9
3 u - 2 u = 12 + 9
1 u = 21
Total number of boys in the end
= 3 u + 7
= 3 x 21 + 7
= 63 + 7
= 70
Total number of pupils in the end
= 3 u + 7 + 2 u + 12
= 5 u + 19
= 5 x 21 + 19
= 124
Fraction of the pupils who were boys in the end
=
70124 =
3562 Answer(s):
3562