Question 514259
Mean score of a class is 70, mean score of boys is 60 and mean score of girls is 75. What's the percentage of girls in the class ???
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Suppose there are x girls and y boys in the class
Suppose the sum of the girls' scores is A and the sum of the boy's score is B 
</pre>
Mean score of a class is 70,
<pre>
That translates as

{{{("SUM_OF_SCORES_OF_GIRLS_AND_BOYS")/("NUMBER_OF_GIRLS_AND_BOYS")}}} = 70  

or as {{{(A+B)/(x+y)=70}}}
</pre>
mean score of boys is 60 
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That translates as

{{{("SUM_OF_SCORES_OF_BOYS")/("NUMBER_OF_BOYS")}}} = 60 

or as {{{B/y = 60}}}
</pre>
and mean score of girls is 75. 
<pre>
That translates as

{{{("SUM_OF_SCORES_OF_GIRLS")/("NUMBER_OF_GIRLS")}}} = 75

or as {{{A/x=75}}}
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What's the percentage of girls in the class ???
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That question translates as

What is {{{"NUMBER_OF_GIRLS"/"NUMBER_OF_GIRLS_AND_BOYS"}}}"?

What is {{{x/(x+y)}}}?

So we have this system of equations:

{{{system((A+B)/(x+y)=70,
B/y = 60,
A/x=75)}}} and we want to find {{{x/(x+y)}}}

We want to eliminate A and B because {{{x/(x+y)}}}
doesn't contain them.
 
Clear them all of fractions:

{{{system(A+B=70x+70y,
B = 60y,
A=75x)}}} and we want to find {{{x/(x+y)}}}

Substitute 60y for B and 75x for A in the first one:

{{{A+B=70x+70y}}}
{{{75x+60y=70x+70y}}}
{{{5x=10y}}}
{{{x=2y}}}

We want to find {{{x/(x+y)}}}

So we substitute 2y for x

{{{(2y)/(x+y)=(2y)/(2y+y)=(2y)/(3y)=2/3}}}

So {{{2/3}}}rd of the class are girls.  

What percentage is that?  {{{66&2/3}}}%.

Edwin</pre>