document.write( "Question 890891: A survey shows that 20% of a population are left-handed, 60% of the left-handed people are men, while 55% of the right-handed people are women. Find the percentage of left-handed women, and right-handed men.\r
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Algebra.Com's Answer #539461 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "       | RIGHT- |  LEFT- |        |\r\n" );
document.write( "       | HANDED | HANDED | TOTALS |\r\n" );
document.write( "-------------------------|--------|\r\n" );
document.write( "MEN    |   A    |   B    |  A+B   |   \r\n" );
document.write( "-------|-----------------|--------|\r\n" );
document.write( "WOMEN  |   C    |   D    |  C+D   |\r\n" );
document.write( "----------------------------------|\r\n" );
document.write( "TOTALS |  A+C   |  B+D   | 100%=1 | \r\n" );
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document.write( "Let A,B,C,D be the percentages of people in each \r\n" );
document.write( "of the four categories, the total of all being \r\n" );
document.write( "100% or 1.\r\n" );
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document.write( "So          A+B+C+D = 1\r\n" );
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document.write( "20% of a population are left-handed, \r\n" );
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document.write( "       .20(A+B+C+D) = B+D\r\n" );
document.write( ".20A+.20B+.20C+.20D = B+D\r\n" );
document.write( ".20A-.80B+.20C-.80D = 0\r\n" );
document.write( "        2A-8B+2C-8D = 0\r\n" );
document.write( "          A-4B+C-4D = 0 \r\n" );
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document.write( "60% of the left-handed people are men,\r\n" );
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document.write( "           .60(B+D) = B\r\n" );
document.write( "          .60B+.60D = B\r\n" );
document.write( "         -.40B+.60D = 0\r\n" );
document.write( "             -4B+6D = 0  \r\n" );
document.write( "             -2B+3D = 0\r\n" );
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document.write( " while 55% of the right-handed people are women. \r\n" );
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document.write( "           .55(A+C) = C\r\n" );
document.write( "          .55A+.55C = C\r\n" );
document.write( "          .55A-.45C = 0\r\n" );
document.write( "            55A-45C = 0\r\n" );
document.write( "             11A-9C = 0\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "          A+ B +C +D = 1\r\n" );
document.write( "          A-4B +C-4D = 0\r\n" );
document.write( "           -2B   +3D = 0\r\n" );
document.write( "        11A   -9C    = 0\r\n" );
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document.write( "Solve that system by any method, and get\r\n" );
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document.write( "A = 0.36, or 36% of the people are right-handed men. \r\n" );
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document.write( "B = 0.12, or 12% of the people are left-handed men.  \r\n" );
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document.write( "C = 0.44, or 44% of the people are right-handed women.\r\n" );
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document.write( "D = 0.08, or  8% of the people are left-handed women. \r\n" );
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\n" ); document.write( "Find the percentage of left-handed women, and right-handed men
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document.write( " 8% of the people are left-handed women.\r\n" );
document.write( "36% of the people are right-handed men.\r\n" );
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document.write( "Edwin
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