document.write( "Question 1185605: Lydia and Nazeerah were walking to school when they spotted a herd of 30 cows and
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Algebra.Com's Answer #816434 by Edwin McCravy(20064) $\"\"$ $\"About$

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Question 1185605
\n" ); document.write( "Lydia and Nazeerah were walking to school when they spotted a herd of 30 cows
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\n" ); document.write( "number of cows and the number of ducks on the farm.
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document.write( "The easy way requires no algebra, just basic arithmetic.\r\n" );
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document.write( "If the 30 animals had all been ducks, there would have been only 60 legs. The\r\n" );
document.write( "extra 32 legs were pairs of hind legs belonging to 16 cows.  So there were 16\r\n" );
document.write( "cows and 30-16 or 14 ducks.\r\n" );
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document.write( "But your teacher probably won't accept that easy way and expects you to use\r\n" );
document.write( "algebra.\r\n" );
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document.write( "Let c = the number of cows\r\n" );
document.write( "Let d = the number of ducks\r\n" );
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document.write( "Then \r\n" );
document.write( "the number of legs on the cows = 4c\r\n" );
document.write( "the number of legs on the ducks = 2d\r\n" );
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document.write( "So the system is\r\n" );
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document.write( "Multiply the first equation by -2 to eliminate d\r\n" );
document.write( "and add the equations term-by-term:\r\n" );
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document.write( "-2c-2d = -60\r\n" );
document.write( " 4c+2d =  92\r\n" );
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document.write( " 2c    =  32\r\n" );
document.write( "  c    =  16    <-- so there were 16 cows.\r\n" );
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document.write( "Substitute in c+d = 30\r\n" );
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document.write( "   c+d = 30\r\n" );
document.write( "  16+d = 30\r\n" );
document.write( "     d = 14     <-- so there were 14 ducks. \r\n" );
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document.write( "Edwin

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