document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199034>Question 1199034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investment of ​$37000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned​ 8% interest, the second​ 6%, and the third​ 9%. Total interest from the investments was $3030 The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832819 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=832819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are several ways you could set this up directly using three variables for the amounts in each investment.  But that would require three equations, and some method for solving a system of three equations.<br><BR>\n" );
document.write( "I always prefer to take a little time to process the given information so that I can set up the problem using a single variable.  Because of the way the information is given in this problem, that takes some effort; but I feel it is worth it.<br><BR>\n" );
document.write( "I hope you get responses from other tutors showing different ways of setting up and solving the problem.<br><BR>\n" );
document.write( "Given the information that the interest from the investment at 8% is 6 times the interest from the investment at 6%, do some mental arithmetic (or use formal algebra) to determine that the amount invested at 8% is 4.5 times the amount invested at 6%.  (8% of 4.5x is 6 times 6% of x...)<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "let 2x = amount invested at 6%<BR>\n" );
document.write( "then 9x = amount invested at 8%<BR>\n" );
document.write( "then 37000-11x = amount invested at 9%<br><BR>\n" );
document.write( "Note I chose 2x and 9x, instead of x and 4.5x, to represent the amounts invested at 6% and 8%.  That's just a personal preference for avoiding fractions or decimals in my equations....<br><BR>\n" );
document.write( "The total interest was $3030:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.06%282x%29%2B.08%289x%29%2B.09%2837000-11x%29=3030 ALIGN=MIDDLE  ALT=\".06%282x%29%2B.08%289x%29%2B.09%2837000-11x%29=3030\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.12x%2B.72x%2B3330-.99x=3030 ALIGN=MIDDLE  ALT=\".12x%2B.72x%2B3330-.99x=3030\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300=.15x ALIGN=MIDDLE  ALT=\"300=.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=300%2F.15=2000 ALIGN=MIDDLE  ALT=\"x=300%2F.15=2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amounts invested at the three rates were<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "2x = $4000 at 6%<BR>\n" );
document.write( "9x = $18000 at 8%<BR>\n" );
document.write( "$37000-11x = $15000 at 9%<br><BR>\n" );
document.write( "CHECK: .06(4000)+.08(18000)+.09(15000) = 240+1440+1350 = 3030<br><BR>\n" );
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