document.write( "Question 1162620: Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate \n" ); document.write( "

Algebra.Com's Answer #786565 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.
\n" ); document.write( "The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same
\n" ); document.write( "as the income from the 8% investment. Find the amount invested at each rate.
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document.write( "In this problem, the key phrase is that saying  \r\n" );
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document.write( "        The income from the 5% and 6% investments is the same as the income from the 8% investment.\r\n" );
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document.write( "It means that the income from 8% investment is half of the total interest of $1600, i.e.  $800.\r\n" );
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document.write( "Next, since the interest of the 8% investment is $800, it means that the amount of the 8% investment is   = 10000 dollars.\r\n" );
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document.write( "Thus, we just know that the 8% investment was $10000; hence, the parts invested at 5% and 6%, make the rest $25000-$10000 = $15000.\r\n" );
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document.write( "Doing in this way, we just reduced the problem from 3 unknowns to only 2,\r\n" );
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document.write( "and the rest of the problem can be solved using one unknown, only.\r\n" );
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document.write( "Let x be the amount invested at 6%;  then the amount invested at 5% is  (15000-x) dollars.\r\n" );
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document.write( "The total interest equation for these two parts is\r\n" );
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document.write( "    0.05*(15000-x) + 0.06x = 800  dollars     (another half of $1600).\r\n" );
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document.write( "From this equation,\r\n" );
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document.write( "    x =  = 5000.\r\n" );
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document.write( "Thus we have the ANSWER :  $5000 was invested at 6%;  15000-5000 = 10000 dollars was invested at 5%  and  $10000 was invested at 8%.\r\n" );
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document.write( "CHECK.  0.06*5000 + 0.05*10000 + 0.08*10000 = 1600 dollars,\r\n" );
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document.write( "        which is precisely correct total interest.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The major lesson to learn is that the problem can be solved using one unknown ONLY (!)\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( " - Advanced word problems to solve using a single linear equation\r
\n" ); document.write( "\n" ); document.write( " - HOW TO algebreze and solve these problems using one equation in one unknown \r
\n" ); document.write( "\n" ); document.write( "in this site and find there other numerous similar solved problems.\r
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