Question 94777: 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 ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=the number of boys and girls involved in the project initially
Then 0.6x=number of boys involved initially
And 0.4x=number of girls involved initially
When the professor made changes in the group, he added six boys and subtracted six girls thus the total number (x) remained the same. So now we have:
0.6x+6=number of boys involved after the changes
---and this equals 0.75x
0.4x-6=number of girls involved after the changes
---and this equals 0.25x
So we have two equations, either of which will yield the correct answer
We'll solve the first one:
0.6x+6=0.75x
0.15x=6
x=40--------------------number of boys and girls involved in the project initially
0.6x=0.6(40)=24-----------------number of boys
40-24=16------------------------number of girls
CK
24+6=30 which is 75% of 40
16-6=10 which is 25% of 40
Hope this helps---ptaylor
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