SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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      Log On


   

Question 1210633: 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?
Answer by ikleyn(53930) About Me  (Show Source):
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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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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

    %2870-x%29%2F%2830-x%29 = 5%2F1.


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.    ANSWER

Solved.