SOLUTION: In a class 40% are girls and the rest are boys. If 15 girls are added in the class,then 52% girls would be there. Find the number of boys and girls in the beginning?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a class 40% are girls and the rest are boys. If 15 girls are added in the class,then 52% girls would be there. Find the number of boys and girls in the beginning?      Log On


   

Question 917735: In a class 40% are girls and the rest are boys. If 15 girls are added in the class,then 52% girls would be there. Find the number of boys and girls in the beginning?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x for girls, y for boys

system(x/(x+y)=0.4,y/(x+y)=0.6)
but x+y is not known

Concentrate just on how many girls.
Let p be number of students.
x%2Fp=0.4

Add 15 more girls.
%28x%2B15%29%2F%28p%2B15%29=0.52

Also you expect x%2By=p

The description gives this system:
highlight_green%28system%28x%2Fp=0.4%2C%28x%2B15%29%2F%28p%2B15%29=0.52%2Cx%2By=p%29%29

system%28x=0.4p%2Cx%2B15=0.52%28p%2B15%29%2Cx%2By=p%29
-
system%28x=0.4p%2Cx%2B15=0.52p%2B7.8%2Cx%2By=p%29
-
highlight_green%28system%28x=0.4p%2Cx%2B7.2=0.52p%2Cx%2By=p%29%29

Use the first two equations to solve for x and p using substitution.
0.4p%2B7.2=0.52p
7.2=0.12p
highlight%28p=60%29
-
x=0.4p
x=%280.4%29%2860%29
highlight%28x=24%29

Now p and x are known.
x%2By=p
y=p-x
y=60-24
highlight%28y=36%29

RESULT:
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Girls,24
Boys,36
How Many Students, 60
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