document.write( "Question 429409: You invested money in two funds. Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330. This year, the first fund paid a 12% dividend and the second only 2% and you received a total of $1500. How much money did you invest in each fund? \n" ); document.write( "

Algebra.Com's Answer #853186 by ikleyn(53538) $\"\"$ $\"About$

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\n" ); document.write( "You invested money in two funds.
\n" ); document.write( "Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.
\n" ); document.write( "This year, the first fund paid a 12% dividend and the second only 2% and you received a total of $1500.
\n" ); document.write( "How much money did you invest in each fund?
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect.\r
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document.write( "Write equations for the annual dividends for the 1st year and for the 2nd year,\r\n" );
document.write( "as you read the problem\r\n" );
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document.write( "    0.08x + 0.05y = 1330    (1)\r\n" );
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document.write( "    0.12x + 0.02y = 1500    (2)\r\n" );
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document.write( "Multiply equation (1) by 2 (both sides).  Multiply equation (2) by 5 (both sides).  You will get\r\n" );
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document.write( "    0.16x + 0.10y = 2660     (1')\r\n" );
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document.write( "    0.60x + 0.10y = 7500     (2')\r\n" );
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document.write( "From equation (2'), subtract equation (1').  You will get\r\n" );
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document.write( "     0.44x    = 7500 - 2660\r\n" );
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document.write( "     0.44x    =     4840\r\n" );
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document.write( "         x    =     4840/0.44 = 11000.\r\n" );
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document.write( "Then from equation (1)\r\n" );
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document.write( "    y =  = 9000.\r\n" );
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document.write( "CHECK.  Equation (1), left side  0.08*11000 + 0.05*9000 = 1330  dollars.   ! correct !\r\n" );
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document.write( "        Equation (2), left side  0.12*11000 + 0.02*9000 = 1500  dollars.   ! correct !\r\n" );
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document.write( "ANSWER.  $11000 were invested in the first fund  and  $9000  were invested in the second fund.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly by the Elimination method.\r
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