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

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Question 105881: A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't 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 Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Originally in the group,
1.B%2F%28B%2BG%29=60%2F100
where B-boys and G-girls.
Then the percentage changed to
2.%28B%2B6%29%2F%28%28B%2B6%29%2B%28G-6%29%29=75%2F100
Our two equations are then,
1.B%2F%28B%2BG%29=60%2F100
2.%28B%2B6%29%2F%28B%2BG%29=75%2F100
Re-writing both equations, you get,
1.B%2BG=100B%2F60
2.B%2BG=100%28B%2B6%29%2F75 or
100B%2F60=100%28B%2B6%29%2F75
75B=60%28B%2B6%29
75B=60B%2B360%29
15B=360
B=24
From 1,
1.B%2BG=100B%2F60
24%2BG=100%2824%29%2F60
24%2BG=100%2824%29%2F60
24%2BG=40
G=16
Check your answer.
Originally there were 24 boys and 16 girls and the ratio of boys to girls was 60%.
24%2F%2824%2B16%29=60%2F100
24%2F40=0.6
0.6=0.6
Good answer.
Then 6 more boys, 6 less girls and the ratio of boys to girls was 75%.
%2824%2B6%29%2F%2824%2B6%2B16-6%29=75%2F100
30%2F40=0.75
0.75=0.75
Good answer.
Final answer : 24 boys, 16 girls.