SOLUTION: In a school, there are 12% girls. If 5boys and 15girls are newly admitted to the school, the percentage of girls becomes 15. What is the total strength of the school? Z

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Question 981206: In a school, there are 12% girls. If 5boys and 15girls are newly admitted to the school, the percentage of girls becomes 15. What is the total strength of the school? Z
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Before the additions, x girls, y boys.
highlight_green%28x%2F%28x%2By%29=0.12%29
x=0.12x%2B0.12y
100x=12x%2B12y
88x=12y
22x=3y


The additions;
highlight_green%28%28x%2B15%29%2F%28x%2B15%2By%2B5%29=0.15%29
%28x%2B15%29%2F%28x%2By%2B20%29=0.15
x%2B15=0.15%28x%2By%2B20%29
100x%2B1500=15x%2B15y%2B15%2A20
85x%2B1500=15y%2B15%2A20
85x=15y%2B15%2A20-1500
85x-15y=300-1500
15y-85x=1200
3y-17x=240

System of equations
system%2822x=3y%2C3y-17x=240%29
Both of which have the term 3y, making finding of x somewhat easy to do.
22x=240%2B17x
5x=240
x=24%2A2%2A5%2F5
highlight%28x=48%29-----original count of the girls.
-
22x=3y
22x%2F3=y
y=22%2A48%2F3
y=22%2A16
highlight%28y=352%29------original count of the boys.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

In a school, there are 12% girls. If 5boys and 15girls are newly admitted to the school, the percentage of girls becomes 15. What is the total strength of the school? Z
Let number of students in school be S

If originally there were 12% girls, then original number of girls was: .12S

After addition of 15 girls, new number of girls = .12S + 15

New number of students: S + 5 + 15, or S + 20

Equation to form: New_number_of_girls%2FNew_number_of_students+=+New_percentage_of_girls

This translates to: %28.12S+%2B+15%29%2F%28S+%2B+20%29+=+.15

 .15(S + 20) = .12S + 15 -------- Cross-multiplying

    .15S + 3 = .12S + 15

 .15S - .12S = 15 - 3

        .03S = 12

S, or original number of students = 12%2F.03, or highlight_green%28400%29