SOLUTION: A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls could not turn up, so the professor had to make some chan

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Question 3113: A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls could not turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.
Answer by glabow(165) About Me  (Show Source):
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The ratio of boys to girls originally was 6/10.
Let x be the original number of boys.
Let y be the original number of girls.
Then x%2F%28x%2By%29+=+6%2F10
And 10x+=+6x+%2B+6y
4x=6y
y+=+%282%2F3%29x
After six girls left, making y-6, he added six boys, making x+6.
The ratio was now 3/4.
Then %28x%2B6%29%2F%28x%2By%29=3%2F4
This becomes
4%28x%2B6%29=3%28x%2By%29
4x+%2B24=3x%2B3y
x%2B24=3y
%281%2F3%29x%2B8=y
Setting the expressions in x as equal gives
%281%2F3%29x+%2B8=%282%2F3%29x
8+=+%281%2F3%29x
24+=+x
Putting this value in the first equation gives
y=16
So there were originally 24 boys and 16 girls, total 40.
24/40 = .6 = 60%
Later, after add/drop, there were 30 boys and 10 girls, total 40.
30/40 = .75 = 75%