document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198745>Question 198745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One year ago Walt invested $12000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?\r<BR>\n" );
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document.write( "I do not know where to place what number in the formula equation<BR>\n" );
document.write( "ax2 + bx + c = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149247 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: you do NOT use the quadratic formula here...\r<BR>\n" );
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document.write( "Let x=Amount he invested at 7% and y=Amount he invested at 9%\r<BR>\n" );
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document.write( "Since he has a total of $12,000, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=12000 ALIGN=MIDDLE  ALT=\"x%2By=12000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, since he invested some at 7% and the rest at 9%, and received $970, this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.07x%2B0.09y=970 ALIGN=MIDDLE  ALT=\"0.07x%2B0.09y=970\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B9y=97000 ALIGN=MIDDLE  ALT=\"7x%2B9y=97000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 100 to make every number whole.\r<BR>\n" );
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document.write( "So we have the system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=12000%2C7x%2B9y=97000%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=12000%2C7x%2B9y=97000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%28x%2By%29=-7%2812000%29 ALIGN=MIDDLE  ALT=\"-7%28x%2By%29=-7%2812000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-7y=-84000 ALIGN=MIDDLE  ALT=\"-7x-7y=-84000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-7x-7y=-84000%2C7x%2B9y=97000%29 ALIGN=MIDDLE  ALT=\"system%28-7x-7y=-84000%2C7x%2B9y=97000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7x-7y%29%2B%287x%2B9y%29=%28-84000%29%2B%2897000%29 ALIGN=MIDDLE  ALT=\"%28-7x-7y%29%2B%287x%2B9y%29=%28-84000%29%2B%2897000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7x%2B7x%29%2B%28-7y%2B9y%29=-84000%2B97000 ALIGN=MIDDLE  ALT=\"%28-7x%2B7x%29%2B%28-7y%2B9y%29=-84000%2B97000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B2y=13000 ALIGN=MIDDLE  ALT=\"0x%2B2y=13000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=13000 ALIGN=MIDDLE  ALT=\"2y=13000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2813000%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y=%2813000%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6500 ALIGN=MIDDLE  ALT=\"y=6500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-7y=-84000 ALIGN=MIDDLE  ALT=\"-7x-7y=-84000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-7%286500%29=-84000 ALIGN=MIDDLE  ALT=\"-7x-7%286500%29=-84000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6500 ALIGN=MIDDLE  ALT=\"y=6500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-45500=-84000 ALIGN=MIDDLE  ALT=\"-7x-45500=-84000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x=-84000%2B45500 ALIGN=MIDDLE  ALT=\"-7x=-84000%2B45500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45500 ALIGN=MIDDLE  ALT=\"45500\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x=-38500 ALIGN=MIDDLE  ALT=\"-7x=-38500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-38500%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"x=%28-38500%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5500 ALIGN=MIDDLE  ALT=\"x=5500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5500 ALIGN=MIDDLE  ALT=\"x=5500\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6500 ALIGN=MIDDLE  ALT=\"y=6500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that he invested $5,500 at 7% and $6,500 at 9%<BR>\n" );
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