document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=686855>Question 686855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve\r<BR>\n" );
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document.write( "Monico invests a total of $13,000 in two accounts. The first account earned a rate of return of 15% (after a year). However, the second account suffered a 13% loss in the same time period. At the end of one year, the total amount of money gained was $550.00. How much was invested into each account?\r<BR>\n" );
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document.write( "$________ was invested at 15% and <BR>\n" );
document.write( "$________ was invested at -13%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424929 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=424929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> $8000 was invested at 15% and <BR>\n" );
document.write( "$5000 was invested at -13%.<BR>\n" );
document.write( "The way to solve it depends on what you are studying<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF YOU ARE STUDYING SYSTEMS OF LINEAR EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount (in $) invested at 15%<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount (in $) invested at -13%<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%2By=13000%29 ALIGN=MIDDLE  ALT=\"highlight%28x%2By=13000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first account earned $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x ALIGN=MIDDLE  ALT=\"0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (15% of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The second account \"earned\" a negative amount (lost 13%),<BR>\n" );
document.write( "so the \"earnings\" from the second account (in $) were <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.13y ALIGN=MIDDLE  ALT=\"-0.13y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The total earnings (in $) were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.15x-0.13y=550%29 ALIGN=MIDDLE  ALT=\"highlight%280.15x-0.13y=550%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting both equations together, you get the system of equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=13000%2C0.15x-0.13y=550%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=13000%2C0.15x-0.13y=550%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are many ways to solve such a system,<BR>\n" );
document.write( "but the most intuitive way would be by substitution.<BR>\n" );
document.write( "You could solve the first equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13000 ALIGN=MIDDLE  ALT=\"x%2By=13000\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13000-x ALIGN=MIDDLE  ALT=\"y=13000-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and then substitute the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13000-x ALIGN=MIDDLE  ALT=\"13000-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-0.13%2813000-x%29=550 ALIGN=MIDDLE  ALT=\"0.15x-0.13%2813000-x%29=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-0.13%2A13000%2B0.13x=550 ALIGN=MIDDLE  ALT=\"0.15x-0.13%2A13000%2B0.13x=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-1690%2B0.13x=550 ALIGN=MIDDLE  ALT=\"0.15x-1690%2B0.13x=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x-1690=550 ALIGN=MIDDLE  ALT=\"0.28x-1690=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x=550%2B1690 ALIGN=MIDDLE  ALT=\"0.28x=550%2B1690\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x=2240 ALIGN=MIDDLE  ALT=\"0.28x=2240\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2240%2F0.28 ALIGN=MIDDLE  ALT=\"x=2240%2F0.28\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8000%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8000 ALIGN=MIDDLE  ALT=\"8000\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13000-x ALIGN=MIDDLE  ALT=\"y=13000-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13000-8000 ALIGN=MIDDLE  ALT=\"y=13000-8000\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=5000%29 ALIGN=MIDDLE  ALT=\"highlight%28y=5000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "IF YOU HAVE NOT STUDIED SYSTEMS OF EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount (in $) invested at 15%<BR>\n" );
document.write( "amount (in $) invested at -13% = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13000-x ALIGN=MIDDLE  ALT=\"13000-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first account earned $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x ALIGN=MIDDLE  ALT=\"0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (15% of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The second account \"earned\" a negative amount (lost 13%),<BR>\n" );
document.write( "so the \"earnings\" from the second account (in $) were <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.13%2813000-x%29 ALIGN=MIDDLE  ALT=\"-0.13%2813000-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The total earnings (in $) were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.15x-0.13%2813000-x%29=550%29 ALIGN=MIDDLE  ALT=\"highlight%280.15x-0.13%2813000-x%29=550%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you simplify and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-0.13%2813000-x%29=550 ALIGN=MIDDLE  ALT=\"0.15x-0.13%2813000-x%29=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-0.13%2A13000%2B0.13x=550 ALIGN=MIDDLE  ALT=\"0.15x-0.13%2A13000%2B0.13x=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x-1690%2B0.13x=550 ALIGN=MIDDLE  ALT=\"0.15x-1690%2B0.13x=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x-1690=550 ALIGN=MIDDLE  ALT=\"0.28x-1690=550\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x=550%2B1690 ALIGN=MIDDLE  ALT=\"0.28x=550%2B1690\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.28x=2240 ALIGN=MIDDLE  ALT=\"0.28x=2240\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2240%2F0.28 ALIGN=MIDDLE  ALT=\"x=2240%2F0.28\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8000%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "amount (in $) invested at -13% = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13000-x=13000-800=highlight%285000%29 ALIGN=MIDDLE  ALT=\"13000-x=13000-800=highlight%285000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );