SOLUTION: HELP set up and solve. 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 professo

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Question 40785This question is from textbook
: HELP set up and solve.
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.
This question is from textbook

Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call X to the original number of boys and Y to the number of girls. If 60% of the students are boys, this means that:
X%2F%28X%2BY%29+=+0.6
X+=+0.6%28X%2BY%29
X+=+0.6X+%2B+0.6Y
0.4X+=+0.6Y
X+=+%283%2F2%29Y
Now, if we have 6 more boys and 6 less girls, the percentage of boys grows to 75%. So we get that:
+%28X+%2B+6%29%2F%28X%2B6%2BY-6%29+=+0.75
+%28X%2B6%29%2F%28X%2BY%29+=+0.75
X%2B6+=+0.75X+%2B+0.75Y
And now we simply plug X=%283%2F2%29Y into this equation:
%283%2F2%29Y+%2B+6+=+0.75%2A%283%2F2%29Y+%2B+0.75Y
6+=+0.375Y
Y+=+16

X+=+%283%2F2%2916+=+24
So originally there were 16 girls and 24 boys.

I hope this helps!
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