Algebra.Com's Answer #820600 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Hector, Kenny and Elliot went shopping with $2190.
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document.write( "Kenny spent $80 and Hector spent 2/5 of his money.
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document.write( "Hector spent half as much as Elliot and had $160 less than what Elliot had left.
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document.write( "In the end, Kenny and Hector had the same amount of money left.
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document.write( "How much money had Elliot at first?
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document.write( " This problem has unexpectedly twisted formulation (which is a rare case in such problems).\r
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document.write( " So, the major step forward is to algebraize it.\r
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document.write( "Let H, K and E be the amounts the persons had originally.\r\n" );
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document.write( "First equation is obvious\r\n" );
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document.write( " H + K + E = 2190. (1)\r\n" );
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document.write( "Hector spent 2/5 of his money; so, he left with 3/5 of his money.\r\n" );
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document.write( "Kenny spent $80; so Kenny left with (K-80) dollars.\r\n" );
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document.write( "At the end, Kenny and Hector had the same amount, which gives us the second equation\r\n" );
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document.write( "  = K - 80\r\n" );
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document.write( "or\r\n" );
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document.write( " 3H = 5K - 400. (2)\r\n" );
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document.write( "Hector spent half as much as Elliot, which means that Elliot spent twice as much as Hector.\r\n" );
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document.write( "Hence, Elliot spent  .\r\n" );
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document.write( "It means that Elliot left with E -  dollars.\r\n" );
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document.write( "From the problem, at the end Hector had left $160 less than what Elliot had left.\r\n" );
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document.write( "It gives us the last, third equation\r\n" );
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document.write( " + 160 = E - ,\r\n" );
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document.write( "or\r\n" );
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document.write( " 7H - 5E = -800. (3)\r\n" );
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document.write( "Thus we have the system of 3 equations in 3 unknowns\r\n" );
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document.write( " H + K + E = 2190. (1)\r\n" );
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document.write( " 3H - 5K = 400. (2)\r\n" );
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document.write( " 7H - 5E = -800. (3)\r\n" );
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document.write( "So the problem is algebraized.\r\n" );
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document.write( "As I said at the beginning, the major step is to algebraize; solving the system is just technical part.\r\n" );
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document.write( "So, I used one of many existing online solvers www.reshish.com to save my time,\r\n" );
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document.write( "and I got this ANSWER : H= 650; K = 470; E = 1070.\r\n" );
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document.write( "Solved.\r
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