document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262662>Question 262662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Ben invests $4000 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that the interest he receives each year is 4 1/2% of the total amount invested? How would I set that up algebraically to solve? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193486 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=193486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the additional money he has to invest at 5.5% interest.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( ".04 * 4000 + .055 * x = .045 * (4000+x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "160 + .055*x = .045 * (4000 + x)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "160 + .055*x = (.045 * 4000) + (.045 * x)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "160 + .055*x = 180 + .045*x\r<BR>\n" );
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document.write( "subtract .045*x from both sides of the equation and subtract 160 from both sides of the equation to get:\r<BR>\n" );
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document.write( ".055*x - .045*x = 180 - 160\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".01*x = 20\r<BR>\n" );
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document.write( "divide both sides of the equation by .01 to get:\r<BR>\n" );
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document.write( "x = 2000.\r<BR>\n" );
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document.write( "replace x by 2000 in the original equation to confirm the answer is good.\r<BR>\n" );
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document.write( "original equation is:\r<BR>\n" );
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document.write( ".04 * 4000 + .055 * x = .045 * (4000+x)\r<BR>\n" );
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document.write( "substitute 2000 for x to get:\r<BR>\n" );
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document.write( ".04 * 4000 + .055 * 2000 = .045 * 6000\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "160 + 110 = 270\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "270 = 270 which is true, confirming that the value for x is good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "the additional money that he has to invest at 5.5% is $2,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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