document.write( "Question 1197028: An amount of Rs 10000 is put in three investments at the rate of 10% 12% 15% per annum. the combined income is Rs 1310 and combined income of first and secpnd investment is 190 less of the income from third . find each,s investment
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Algebra.Com's Answer #830101 by ikleyn(52866) $\"\"$ $\"About$

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document.write( "       x +     y +     z = 10000    (1)\r\n" );
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document.write( "    0.1x + 0.12y + 0.15z =  1310    (2)\r\n" );
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document.write( "   -0.1x - 0.12y + 0.15z =   190    (3)\r\n" );
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document.write( "Add equations (2) and (3).  You will get\r\n" );
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document.write( "                   0.3z = 1310 + 190 = 1500,   hence  z = 1500/0.3 = 5000.\r\n" );
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document.write( "Substitute z= 5000 into equations (1) and (2).   You will get\r\n" );
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document.write( "       x +     y = 5000    (4)\r\n" );
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document.write( "    0.1x + 0.12y =  560    (5)\r\n" );
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document.write( "Multiply equation (5) by 10; keep equation (4) as is.  You will get then\r\n" );
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document.write( "       x +     y = 5000    (4')\r\n" );
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document.write( "       x +  1.2y = 5600    (5')\r\n" );
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document.write( "Subtract (4') from (5').  You will get\r\n" );
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document.write( "            0.2y =  600;  hence  y = 600/0.2 = 3000.\r\n" );
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document.write( "Now use equation (1) to find x.  Substitute  y= 3000  and  z= 5000 into (1)\r\n" );
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document.write( "    x + 3000 + 5000 = 10000.\r\n" );
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document.write( "It gives  x = 10000 - 3000 - 5000 = 2000.\r\n" );
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document.write( "ANSWER.  $2000 invested at 10%;  $3000 invested at 12%  and  $5000 invested at 15%.\r\n" );
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document.write( "CHECK.   Please check it on your own, substituting the values into equations (2) and (3).\r\n" );
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