document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122870>Question 1122870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maya invested her savings in two investment funds. The <BR>\n" );
document.write( "$4000<BR>\n" );
document.write( " that she invested in Fund A returned a <BR>\n" );
document.write( "10%<BR>\n" );
document.write( " profit. The amount that she invested in Fund B returned a <BR>\n" );
document.write( "3%<BR>\n" );
document.write( " profit. How much did she invest in Fund B, if both funds together returned a <BR>\n" );
document.write( "5%<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 #739049 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=739049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Algebraically....<br><BR>\n" );
document.write( "Let x be the amount invested at 3%.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.03%29%28x%29%2B%28.10%29%284000%29+=+%28.05%29%284000%2Bx%29 ALIGN=MIDDLE  ALT=\"%28.03%29%28x%29%2B%28.10%29%284000%29+=+%28.05%29%284000%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can do the algebra to get the answer.<br><BR>\n" );
document.write( "If an algebraic solution is not required, here is a much faster way to solve a problem like this.<br><BR>\n" );
document.write( "The ratio between the amounts invested in the two places exactly determines where the overall percentage return lies between the two individual percentages.<br><BR>\n" );
document.write( "The 5% return is 5% away from 10% and 2% away from 3%.  That ratio 5:2 means the money must be split in the ratio 5:2.  And since the overall return is close to 3% than to 10%, the larger amount needs to be invested at 3%.<br><BR>\n" );
document.write( "So if x is the amount invested at 3%, we have a proportion:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3A2+=+x%3A4000 ALIGN=MIDDLE  ALT=\"5%3A2+=+x%3A4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2+=+x%2F4000 ALIGN=MIDDLE  ALT=\"5%2F2+=+x%2F4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+20000 ALIGN=MIDDLE  ALT=\"2x+=+20000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10000 ALIGN=MIDDLE  ALT=\"x+=+10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "She invested $10000 in investment B.<br><BR>\n" );
document.write( "CHECK:<br><BR>\n" );
document.write( "10% of $4000 = $400<BR>\n" );
document.write( "3% of $10000 = $300<BR>\n" );
document.write( "Total $400+$300 = $700<br><BR>\n" );
document.write( "5% of $14000 = $700<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );