document.write( "Question 1184444: Ali, Ben, Cain and Dan, shared a sum of money.
\n" ); document.write( "Ali has 1/2 of the total amount of money that Ben, Cain and Dan have.
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\n" ); document.write( "Cain has 1/7 of the total amount of money that Ali, Ben and Dan have.\r
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Algebra.Com's Answer #815039 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Greenestamps did it the most elementary way. Think I'll do it using\r\n" );
document.write( "matrices.  Maybe you've gotten that far.\r\n" );
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document.write( ">>>Ali, Ben, Cain and Dan, shared a sum of money.\r\n" );
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document.write( ">>>Let A,B.C.D be the fractions of their shares.  Then the sum of the\r\n" );
document.write( "four fractions must be 1 (whole).\r\n" );
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document.write( "So \"A%2BB%2BC%2BD\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( ">>>Ali has 1/2 of the total amount of money that Ben, Cain and Dan have.\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"expr%281%2F2%29%28B%2BC%2BD%29\"\r\n" );
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document.write( ">>>Ben has 1/3 of the total amount of money that Ali, Cain and Dan have.\r\n" );
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document.write( "\"B\"\"%22%22=%22%22\"\"expr%281%2F3%29%28A%2BC%2BD%29\"\r\n" );
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document.write( ">>>Cain has 1/7 of the total amount of money that Ali, Ben and Dan have.\r\n" );
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document.write( "\"C\"\"%22%22=%22%22\"\"expr%281%2F7%29%28A%2BB%2BD%29\"\r\n" );
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document.write( "The system is\r\n" );
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document.write( "\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "The matrix is\r\n" );
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document.write( "Do row operations on that to get the row reduced echelon form (RREF)\r\n" );
document.write( "of the matrix above.  Your TI-84 can handle that if you understand the\r\n" );
document.write( "matrix feature.\r\n" );
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document.write( "The RREF matrix form of that is as below\r\n" );
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document.write( "So Ali got 1/3, Ben got 1/4, Cain got 1/8, and Dan got 1/7.\r\n" );
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document.write( "For (b)\r\n" );
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document.write( "Let $S = the total amount,\r\n" );
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document.write( "Then Dan's share was 7/24 of $S\r\n" );
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document.write( "So \"expr%287%2F24%29S=%22%2484%22\"\r\n" );
document.write( "   \"7S=%22%242016%22\"\r\n" );
document.write( "   \"S=%22288%22\" \r\n" );
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document.write( "[Greenestamps was right!]]\r\n" );
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document.write( "Ali got 1/3 of $288 or $96\r\n" );
document.write( "Ben got 1/4 of $288 or $72\r\n" );
document.write( "Cain got 1/8 of $588 or $36\r\n" );
document.write( "Dan got $84\r\n" );
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document.write( "Check:\r\n" );
document.write( "The sum was $96\r\n" );
document.write( "            $72\r\n" );
document.write( "            $36\r\n" );
document.write( "            $84\r\n" );
document.write( "            ---\r\n" );
document.write( "           $288 as we expected.  \r\n" );
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document.write( "Edwin
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