document.write( "Question 1101355: $15,074 is invested part at 14% and the rest at 5% if the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 5% by $1694.07 how much is invested at each rate? Round to two decimal places if necessary \n" ); document.write( "

Algebra.Com's Answer #715950 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "$15,074 is invested part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest
\n" ); document.write( "earned from the amount invested at 5% by $1694.07 how much is invested at each rate? Round to two decimal places if necessary
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document.write( "From the condition, you have THIS system of 2 equations in 2 unknowns\r\n" );
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document.write( "    x +     y = 15074            (1)    (counting investments)\r\n" );
document.write( "0.14x - 0.05y =  1694.07         (2)    (the difference between earnings)\r\n" );
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document.write( "To make your calculations easier, multiply eq(2) by 100 (both sides). The modified system is\r\n" );
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document.write( "    x +     y = 15074            (3)   \r\n" );
document.write( "  14x -    5y = 169407           (4)  \r\n" );
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document.write( "Now multiply eq(3) by 5. The modified system takes the form\r\n" );
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document.write( "   5x +    5y = 5*15074          (5)\r\n" );
document.write( "  14x -    5y = 169407           (4)  \r\n" );
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document.write( "Next add the equations (5) and (6) (both sides).  The terms with 5y will cancel each other, and you will get a single equation for x:\r\n" );
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document.write( "  19x = 5*15074 + 169407 = 244777.\r\n" );
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document.write( "    x =  = 12883.\r\n" );
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document.write( "Answer.  It was invested $12883 at %14.  The rest 15074 - 12883 = 2191 was invested at  5%.\r\n" );
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document.write( "Check.  0.14*12883 - 0.05*2191 = 1694.07.   ! Correct !\r\n" );
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\n" ); document.write( "On investment problems, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Using systems of equations to solve problems on investment\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "Be aware ! Writing by @richwmiller was heavily incorrect. \r
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