document.write( "Question 1119152: Hi, I have a problem that I don't understand how to solve, where there are two different interest rates. Can you help me with this? \r
\n" ); document.write( "\n" ); document.write( "\"Madge invested $10,000 for one year, part at 8% annual interest and the rest at 12% annual interest. Her total interest for the year was $944. How much did she invest at each rate?\"\r
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Algebra.Com's Answer #734613 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let x be the amount invested at 8% (in dollars).\r\n" );
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document.write( "Then the amount invested at 12% is (10000-x) dollars.\r\n" );
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document.write( "The amount x produces the interest equal 0.08*x.\r\n" );
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document.write( "The amount (10000-x) produces  the interest equal 0.12*(10000-x).\r\n" );
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document.write( "Together, these investments produce the total interest of 0.08x + 0.12*(10000-x).\r\n" );
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document.write( "We are given that the total interest is 944 dollars.\r\n" );
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document.write( "It gives you an equation \r\n" );
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document.write( "    0.08x + 0.12*(10000-x) = 944.\r\n" );
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document.write( "Simplify and solve it for x:\r\n" );
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document.write( "   0.08x + 1200 - 0.12x = 944\r\n" );
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document.write( "   -0.04x = 944 - 1200 = -256\r\n" );
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document.write( "   x =  = 6400.\r\n" );
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document.write( "Answer.  $6400 was invested at 8%.  The rest (10000-6400) = 3600 dollars was invested at 12%.\r\n" );
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document.write( "Check.   0.08*6400 + 0.12*3600 = 944.  ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a typical and standard problem on investment.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems on investment, look into 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( "You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
\n" ); document.write( "different methods of solution to the equations (Substitution, Elimination).\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
\n" ); document.write( "
\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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