Question 917735
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/p=0.4}}}


Add 15 more girls.
{{{(x+15)/(p+15)=0.52}}}


Also you expect {{{x+y=p}}}


The description gives this system:
{{{highlight_green(system(x/p=0.4,(x+15)/(p+15)=0.52,x+y=p))}}}


{{{system(x=0.4p,x+15=0.52(p+15),x+y=p)}}}
-
{{{system(x=0.4p,x+15=0.52p+7.8,x+y=p)}}}
-
{{{highlight_green(system(x=0.4p,x+7.2=0.52p,x+y=p))}}}


Use the first two equations to solve for x and p using substitution.
{{{0.4p+7.2=0.52p}}}
{{{7.2=0.12p}}}
{{{highlight(p=60)}}}
-
{{{x=0.4p}}}
{{{x=(0.4)(60)}}}
{{{highlight(x=24)}}}


Now p and x are known.
{{{x+y=p}}}
{{{y=p-x}}}
{{{y=60-24}}}
{{{highlight(y=36)}}}


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