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 change
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Question 131934: 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.
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Let x=total number of boys and girls in the initial project
Then 0.6x=number of boys
And 0.4x= number of girls
Now we know that:
0.6x+6=0.75x subtract 0.6x from each side
0.6x-0.6x+6=0.75x-0.6x collect like terms
0.15x=6 divide both sides by 0.15
x=40 total number of boys and girls in the initial project
Number of boys=0.6*40=24
Number of girls=0.4*40=16
24+16=40
16-6=10 ----number of girls in the final project
10=25% of 40
24+6=30 number of boys in the final project
30=75% of 40
Another way (looking at the girls)
0.4x-6=0.25x subtract 0.4x from each side
0.4x-0.4x-6=0.25x-0.4x collect like terms
-6=-0.15x divide both sides by -0.15
x=40 ----------total number of boys and girls in the initial project
Hope this helps---ptaylor
