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Question 112793: 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 girls. 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!
I THINK THAT YOU HAVE STATED THE PROBLEM INCORRECTLY. IT THINK IT SHOULD READ---"HE ADMITTED SIX BOYS----"---NOT SIX GIRLS. IF HE ADMITTED SIX GIRLS, THE PERCENTAGE OF BOY S WOULD NOT HAVE CHANGED.
Let x=number of boys and girls involved in the project initially
Then 0.6x=number of boys
And 0.4x=number of girls
Now we are told that:
0.4x-6=0.25x subtract 0.4x from both sides
0.4x-0.4x-6=0.25x-0.4x collect like terms
-6=-0.15x divide both sides by -0.15
x=40 ---number of boys and girls involved in the project initially
ANOTHER WAY:
0.6x+6=0.75x subtract 0.6x from both sides
0.15x=6
x=40
CK
60% of 40 =24
40% of 40 =16
16-6=10
24+6=30
10 is 25% of 40
30 is 75% of 40
Hope this helps---ptaylor
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