SOLUTION: Mean score of a class is 70, mean score of boys is 60 and mean score of girls is 75. whats the percentage of girls in the class ???

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Question 514259: Mean score of a class is 70, mean score of boys is 60 and mean score of girls is 75. whats the percentage of girls in the class ???
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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 ???
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

Mean score of a class is 70,
That translates as

%28%22SUM_OF_SCORES_OF_GIRLS_AND_BOYS%22%29%2F%28%22NUMBER_OF_GIRLS_AND_BOYS%22%29 = 70  

or as %28A%2BB%29%2F%28x%2By%29=70

mean score of boys is 60 
That translates as

%28%22SUM_OF_SCORES_OF_BOYS%22%29%2F%28%22NUMBER_OF_BOYS%22%29 = 60 

or as B%2Fy+=+60

and mean score of girls is 75. 
That translates as

%28%22SUM_OF_SCORES_OF_GIRLS%22%29%2F%28%22NUMBER_OF_GIRLS%22%29 = 75

or as A%2Fx=75

What's the percentage of girls in the class ???
That question translates as

What is %22NUMBER_OF_GIRLS%22%2F%22NUMBER_OF_GIRLS_AND_BOYS%22"?

What is x%2F%28x%2By%29?

So we have this system of equations:

system%28%28A%2BB%29%2F%28x%2By%29=70%2C%0D%0AB%2Fy+=+60%2C%0D%0AA%2Fx=75%29 and we want to find x%2F%28x%2By%29

We want to eliminate A and B because x%2F%28x%2By%29
doesn't contain them.
 
Clear them all of fractions:

system%28A%2BB=70x%2B70y%2C%0D%0AB+=+60y%2C%0D%0AA=75x%29 and we want to find x%2F%28x%2By%29

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

A%2BB=70x%2B70y
75x%2B60y=70x%2B70y
5x=10y
x=2y

We want to find x%2F%28x%2By%29

So we substitute 2y for x

%282y%29%2F%28x%2By%29=%282y%29%2F%282y%2By%29=%282y%29%2F%283y%29=2%2F3

So 2%2F3rd of the class are girls.  

What percentage is that?  66%262%2F3%.

Edwin