document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099292>Question 1099292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John has $5000 to invest. Part he wishes to invest in an insured account that gives 4% annual return; however, he would like to invest in a non-insured mutual fund that gives a 7% annual return. How much should he invest in each so that the combined return is 6% annually? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713734 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</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=713734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Here is a different method for solving this kind of problem -- described first informally, then with a formal mathematical process.<br><BR>\n" );
document.write( "Informally...<BR>\n" );
document.write( "The 6% is twice as close to 7% as it is to 4%; that means twice as much must be invested at 7% as at 4%.<BR>\n" );
document.write( "So 2/3 of the $5000 must be invested at 7% and 1/3 of it at 4%.<br><BR>\n" );
document.write( "The same process, formally...<BR>\n" );
document.write( "The process is called alligation.  If you haven't heard of it and are interested in learning more about it, do an internet search...<br><BR>\n" );
document.write( "Start with a \"tic-tac-toe\" game board:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Put the percentages of the two accounts in the top and bottom cells of column 1, and put the combined percentage in the middle cell:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C7%2Cx%2Cx%2Cx%2C6%2Cx%2C4%2Cx%2Cx%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C7%2Cx%2Cx%2Cx%2C6%2Cx%2C4%2Cx%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Working diagonally, put the positive difference between the numbers in column 1 and the number in column 2 in the appropriate cells in column 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C7%2Cx%2C2%2Cx%2C6%2Cx%2C4%2Cx%2C1%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C7%2Cx%2C2%2Cx%2C6%2Cx%2C4%2Cx%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 2 and 1 in column 3 tell you that the money must be invested in the ratio 2:1. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );