document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350065>Question 350065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A book loaned out #250,000, part of it at the rate of 8% annual mortgage interest and the rest at the rate of 18% annual credit card interest.  The interest received on both loans totaled $23,000.  How much was loaned at each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250271 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=250271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Amount of money lent out totals $250,000\r<BR>\n" );
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document.write( "x was loaned at 8% annual compounding assumed.<BR>\n" );
document.write( "y was loaned at 18% annual compounding assumed.\r<BR>\n" );
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document.write( "Interest received on both loans totaled $23,000 for the year.\r<BR>\n" );
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document.write( "You have 2 formulas to work with.\r<BR>\n" );
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document.write( "x + y = 250,000 covers the amount of the loan.<BR>\n" );
document.write( ".08*x + .18*y = 23,000 covers the interest earned for the year.\r<BR>\n" );
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document.write( "Solve both of these equations simultaneously and you will find how much was loaned out at each rate.\r<BR>\n" );
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document.write( "Use first equation to solve for y.\r<BR>\n" );
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document.write( "You get y = 250,000 - x\r<BR>\n" );
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document.write( "Substitute in second equation to get:\r<BR>\n" );
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document.write( ".08 * x + .18 * y = 23,000 becomes:\r<BR>\n" );
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document.write( ".08 * x + .18 * (250,000 - x) = 23,000\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( ".08 * x + .18 * 250,000 - .18 * x = 23,000\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( ".08 * x + 45,000 - .18 * x = 23,000\r<BR>\n" );
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document.write( "Subtract 45,000 from both sides of the equation and combine like terms to get:\r<BR>\n" );
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document.write( "-.1 * x = -22,000\r<BR>\n" );
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document.write( "Divide both sides of the equation by -.1 to get:\r<BR>\n" );
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document.write( "x = 220,000\r<BR>\n" );
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document.write( "This means y = 30,000 because x + y = 250,000\r<BR>\n" );
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document.write( "The book loaned 220,000 at 8% and 30,000 at 18% to make a total interest of 17,600 + 5,400 = 23,000 for the year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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