There were 5 more boys than girls in the music room. Excluding 12 girls, the number of girls was
23 of the number of boys. When another 7 boys joined, what fraction of the students were boys in the end? Give your answer in its simplest form.
|
Boys |
Girls |
Comparing boys and girls at first |
5 more |
|
Before |
3 u |
2 u + 12 |
Change |
+ 7 |
|
After |
3 u + 7 |
2 u + 12 |
Number of boys at first was 5 more than the number of girls. If another 5 girls entered the music room at first, the number of boys and girls at first would be the same.
3 u = 2 u + 12 + 5
3 u - 2 u = 12 + 5
1 u = 17
Total number of boys in the end
= 3 u + 7
= 3 x 17 + 7
= 51 + 7
= 58
Total number of students in the end
= 3 u + 7 + 2 u + 12
= 5 u + 19
= 5 x 17 + 19
= 104
Fraction of the students who were boys in the end
=
58104 =
2952 Answer(s):
2952