Question 1210633
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In a store selling Brand X and Brand Y shoes, some of the 100 pairs of shoes were sold. 
The ratio of the number of Brand X shoes to Brand Y shoes was 7/3 before the sale 
and became 5/1 after the sale. 
If an equal number of shoes were sold from both brands, 
how many total pairs of shoes remained in the store after the sale?
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<pre>
The problem says that initially were there 100 pairs of shoes of the brands X and Y in proportion 7:3.


It means that were there 70 pairs of brand X and 30 pairs of brand Y.


OK.  Next, let x be the number of pairs sold of each brand.


Then for remaining pairs, 70-x and 30-x, we have this proportion

    {{{(70-x)/(30-x)}}} = {{{5/1}}}.


Solve it and find x. For it, cross multiply and then simplify

    70-x = 5(30-x),

    70 - x = 150 - 5x,

    5x - x = 150 - 70,

       4x   =   80,

        x   =   20.


So 20 pairs of each brand were solved. 
Hence, the remaining was 70-20 = 50 pairs of brand X and 30-20 = 10 pairs of brand Y,
giving the total 50+10 = 60 remaining pairs.    <U>ANSWER</U>
</pre>

Solved.