document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #854567 by ikleyn(53930) $\"\"$ $\"About$

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\n" ); document.write( "In a store selling Brand X and Brand Y shoes, some of the 100 pairs of shoes were sold.
\n" ); document.write( "The ratio of the number of Brand X shoes to Brand Y shoes was 7/3 before the sale
\n" ); document.write( "and became 5/1 after the sale.
\n" ); document.write( "If an equal number of shoes were sold from both brands,
\n" ); document.write( "how many total pairs of shoes remained in the store after the sale?
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document.write( "The problem says that initially were there 100 pairs of shoes of the brands X and Y in proportion 7:3.\r\n" );
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document.write( "It means that were there 70 pairs of brand X and 30 pairs of brand Y.\r\n" );
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document.write( "OK.  Next, let x be the number of pairs sold of each brand.\r\n" );
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document.write( "Then for remaining pairs, 70-x and 30-x, we have this proportion\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Solve it and find x. For it, cross multiply and then simplify\r\n" );
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document.write( "    70-x = 5(30-x),\r\n" );
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document.write( "    70 - x = 150 - 5x,\r\n" );
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document.write( "    5x - x = 150 - 70,\r\n" );
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document.write( "       4x   =   80,\r\n" );
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document.write( "        x   =   20.\r\n" );
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document.write( "So 20 pairs of each brand were solved. \r\n" );
document.write( "Hence, the remaining was 70-20 = 50 pairs of brand X and 30-20 = 10 pairs of brand Y,\r\n" );
document.write( "giving the total 50+10 = 60 remaining pairs.    ANSWER\r\n" );
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