document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128896>Question 1128896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investment of $4500 is made at an interest rate of 8% for one year. How much money must be invested at a rate 5% so that the total interest earned is 6% of the total investment?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745430 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "By traditional algebra....<br><BR>\n" );
document.write( "8% of $4500, plus 5% of an unknown amount x, equals 6% of the total, $4500+x:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.08%284500%29%2B.05%28x%29+=+.06%284500%2Bx%29 ALIGN=MIDDLE  ALT=\".08%284500%29%2B.05%28x%29+=+.06%284500%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That equation is relatively easy to solve, although the decimals might make it take some time.<br><BR>\n" );
document.write( "Here is a MUCH easier way to solve the problem (assuming a formal algebraic solution is not required).<br><BR>\n" );
document.write( "(1) The overall average of 6% is \"twice as close\" to 5% as it is to 8%.<BR>\n" );
document.write( "(2) Therefore, twice as much must be invested at 5% as at 8%.<BR>\n" );
document.write( "(3) Since $4500 is invested at 8%, the amount required to be invested at 5% is 2*$4500 = $9000.<br><BR>\n" );
document.write( "ANSWER: $9000 at 5%<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".08(4500)+.05(9000) = 360+450 = 810<BR>\n" );
document.write( ".06(13500) = 810 </SPAN>\n" );
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