document.write( "Question 1205783: A lawn-care technician wants to spread a 200-lb seed mixture that is 50% bluegrass. If the technician
\n" ); document.write( "has on hand a mixture that is 75% bluegrass and a mixture that is 10% bluegrass, how many pounds of
\n" ); document.write( "each mixture are needed to make 200 lb of the 50% mixture? Round to the nearest whole pound. \n" ); document.write( "

Algebra.Com's Answer #842814 by Edwin McCravy(20056) $\"\"$ $\"About$

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A lawn-care technician wants to spread a 200-lb seed mixture
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\n" ); document.write( "many pounds of each mixture are needed to make 200 lb of the
\n" ); document.write( "50% mixture? Round to the nearest whole pound.
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document.write( "                      lbs of      part     lbs of bluegrass\r\n" );
document.write( "                      mixture   bluegrass    in mixture\r\n" );
document.write( "stronger mixture         x         0.75         0.75x\r\n" );
document.write( "weaker mixture           y         0.10         0.10y\r\n" );
document.write( "final medium mixture    200        0.50         0.50(200)=100\r\n" );
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document.write( "The equations come from the first and last columns:\r\n" );
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document.write( "Simplify the second equation by clearing the decimals by multiplying\r\n" );
document.write( "through by 100\r\n" );
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document.write( "You can solve this simpler by elimination:\r\n" );
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document.write( "Multiply the first equation by -10 to make the y's cancel:\r\n" );
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document.write( "Add the two equations term by term\r\n" );
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document.write( "65x = 8000\r\n" );
document.write( "  x = 123.0769231 round to 123 of the stronger mixture\r\n" );
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document.write( "Since that's not easy to substitute, go back and\r\n" );
document.write( "multiply the first equation by -75 to make the y's cancel:\r\n" );
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document.write( "Add the two equations term by term\r\n" );
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document.write( "-65y = -5000\r\n" );
document.write( "  y = 76.92307692 round to 77 pounds of the weaker.\r\n" );
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document.write( "As a partial mental check, think of the fact that it is logical\r\n" );
document.write( "that you would use more of the stronger and less of the weaker, \r\n" );
document.write( "because 50% is closer to 75% than it is to 10%.  That's not a\r\n" );
document.write( "perfect check, but if we had gotten less stronger than weaker, \r\n" );
document.write( "we would known such an answer would be wrong.\r\n" );
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document.write( "Edwin

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