document.write( "Question 333707: In a group of five friends, the sums of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest? \n" ); document.write( "

Algebra.Com's Answer #239121 by Edwin McCravy(20056) $\"\"$ $\"About$

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In a group of five friends, the sums of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest?
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document.write( "Let the five ages be A, B, C, D, and E.\r\n" );
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document.write( "A + B + C + D = 124\r\n" );
document.write( "A + B + C + E = 128\r\n" );
document.write( "A + B + D + E = 130\r\n" );
document.write( "A + C + D + E = 136\r\n" );
document.write( "B + C + D + E = 142\r\n" );
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document.write( "We consider that as this system, putting in all the \r\n" );
document.write( "understood 1's and 0's\r\n" );
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document.write( "1A + 1B + 1C + 1D + 0E = 124\r\n" );
document.write( "1A + 1B + 1C + 0D + 1E = 128\r\n" );
document.write( "1A + 1B + 0C + 1D + 1E = 130\r\n" );
document.write( "1A + 0B + 1C + 1D + 1E = 136\r\n" );
document.write( "0A + 1B + 1C + 1D + 1E = 142\r\n" );
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document.write( "Now we make the augmented matrix:\r\n" );
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document.write( "Using my TI-84 I get for the rref of that matrix:\r\n" );
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document.write( "A=23, B=29, C=35, D=37, E=41.\r\n" );
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document.write( "The youngest age is A, which is 23. \r\n" );
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document.write( "Edwin

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