document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103832>Question 1103832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Charlie invested his savings in two investment funds. The <BR>\n" );
document.write( "$4000<BR>\n" );
document.write( " that he invested in Fund A returned a <BR>\n" );
document.write( "2%<BR>\n" );
document.write( " profit. The amount that he invested in Fund B returned a <BR>\n" );
document.write( "5%<BR>\n" );
document.write( " profit. How much did he invest in Fund B, if both funds together returned a <BR>\n" );
document.write( "3%<BR>\n" );
document.write( " profit?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718531 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=718531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "NOTE: I misread the problem, thinking that the $4000 was the total amount invested.<br><BR>\n" );
document.write( "Skip down to the ================= to see the revised solution.<br><BR>\n" );
document.write( "Here, first, is the quick way to get the answer to a problem like this.  We can look at the slow, formal algebraic method later.<br><BR>\n" );
document.write( "The 3% average return is twice as close to 2% as it is to 5%.  That means twice as much was invested at 2% as at 5%.<br><BR>\n" );
document.write( "That means the $4000 was invested with 2/3 of it at 2% and 1/3 of it at 5%.<br><BR>\n" );
document.write( "1/3 of $4000 is $1333.33  (which indicates \"bad\" numbers are used for this problem....)<BR>\n" );
document.write( "2/3 of $4000 is $2666.67<br><BR>\n" );
document.write( "So the amount he invested in Fund B was $1333.33.<br><br><BR>\n" );
document.write( "Now the standard algebraic solution method....<br><BR>\n" );
document.write( "\"The return for x amount in Fund B at 5%, plus the return for the rest (4000-x) in Fund A at 2%, yielded an average return of 3% on the total investment\".<BR>\n" );
document.write( "Translated into an algebraic equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%28x%29%2B.02%284000-x%29+=+.03%284000%29 ALIGN=MIDDLE  ALT=\".05%28x%29%2B.02%284000-x%29+=+.03%284000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [note the form for each term on both sides of the equation is the same: (interest rate)*(amount)]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%29%2B2%284000-x%29+=+3%284000%29 ALIGN=MIDDLE  ALT=\"5%28x%29%2B2%284000-x%29+=+3%284000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   [simplify the calculation by getting rid of the decimals]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B8000-2x+=+12000 ALIGN=MIDDLE  ALT=\"5x%2B8000-2x+=+12000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+4000 ALIGN=MIDDLE  ALT=\"3x+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1333.33 ALIGN=MIDDLE  ALT=\"x+=+1333.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount invested in Fund B at 5% was $1333.33.<br><BR>\n" );
document.write( "========================================================================<BR>\n" );
document.write( "Here, first, is the quick way to get the answer to a problem like this.  We can look at the slow, formal algebraic method later.<br><BR>\n" );
document.write( "The 3% average return is twice as close to 2% as it is to 5%.  That means twice as much was invested at 2% as at 5%.<br><BR>\n" );
document.write( "Since twice as much was invested in Fund A as in Fund B, the amount he invested in Fund B was $2000.<br><br><BR>\n" );
document.write( "Now the standard algebraic solution method....<br><BR>\n" );
document.write( "\"The return for x amount in Fund B at 5%, plus the return for the 4000 in Fund A at 2%, yielded an average return of 3% on the total investment\".<BR>\n" );
document.write( "Translated into an algebraic equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%28x%29%2B.02%284000%29+=+.03%284000%2Bx%29 ALIGN=MIDDLE  ALT=\".05%28x%29%2B.02%284000%29+=+.03%284000%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [note the form for each term on both sides of the equation is the same: (interest rate)*(amount)]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%29%2B2%284000%29+=+3%284000%2Bx%29 ALIGN=MIDDLE  ALT=\"5%28x%29%2B2%284000%29+=+3%284000%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   [simplify the calculation by getting rid of the decimals]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B8000+=+12000%2B3x ALIGN=MIDDLE  ALT=\"5x%2B8000+=+12000%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+4000 ALIGN=MIDDLE  ALT=\"2x+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2000 ALIGN=MIDDLE  ALT=\"x+=+2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount invested in Fund B at 5% was $2000.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );