document.write( "Question 1092440: Student Loans. Dimitri’s two student loans total $9000. One loan is at 4.5% simple interest and the other is at\r
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Algebra.Com's Answer #707037 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It is a standard problem on investments.\r\n" );
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document.write( "If x is the amount at 4.5% and y is amount at 5.5%, then you have this system of two equations for two unknowns \r\n" );
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document.write( "     x +      y = 9000,      (1)     (total amount)\r\n" );
document.write( "0.045x + 0.055y = 447.       (2)     (owes)\r\n" );
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document.write( "To solve it, first multiply eq(2) by 10000. Then the system takes the form\r\n" );
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document.write( "     x +     y = 9000,       (1) \r\n" );
document.write( "   45x +   55y = 447000.     (2) \r\n" );
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document.write( "Now  from eq(1) express   y = 9000 - x  and substitute into eq(2). You will get a single equation for x\r\n" );
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document.write( "45x + 55(9000-x) = 447000.\r\n" );
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document.write( "Simplify it step by step and solve for x:\r\n" );
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document.write( "45x + 495000 - 55x = 447000,\r\n" );
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document.write( "-10x = 447000 - 495000 = -48000  ====>  x =  = 4800.\r\n" );
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document.write( "Thus the amount at 4.5% is just found. It is $4800.\r\n" );
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document.write( "Then the second amount is the rest of 9000:  y = 9000 - 4800 = 4200.\r\n" );
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document.write( "Answer.  $4800 at 4.5%  and  $4200 at 5.5%.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson \r
\n" ); document.write( "\n" ); document.write( " - Using systems of equations to solve problems on investment\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\r
\n" ); document.write( "\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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