document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190617>Question 190617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> # 9.  Mike invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest. How much did he invest at each rate?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143075 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=143075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 9 \r<BR>\n" );
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document.write( "Q: <font color=red> Mike invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest. How much did he invest at each rate? </font>\r<BR>\n" );
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document.write( "A:\r<BR>\n" );
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document.write( "Let \r<BR>\n" );
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document.write( "x = amount of money Mike invests at 8%\r<BR>\n" );
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document.write( "y = amount of money Mike invests at 12%\r<BR>\n" );
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document.write( "Since \"Mike invested $7000 for one year.\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=7000 ALIGN=MIDDLE  ALT=\"x%2By=7000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, because \"He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest.\", this translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.08x%2B0.12y=764 ALIGN=MIDDLE  ALT=\"0.08x%2B0.12y=764\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiplying every term by 100 gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B12y=76400 ALIGN=MIDDLE  ALT=\"8x%2B12y=76400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=7000%2C8x%2B12y=76400%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=7000%2C8x%2B12y=76400%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve this system by substitution\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=7000 ALIGN=MIDDLE  ALT=\"x%2By=7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7000-x ALIGN=MIDDLE  ALT=\"y=7000-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B7000 ALIGN=MIDDLE  ALT=\"y=-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B7000 ALIGN=MIDDLE  ALT=\"y=-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <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 with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B7000 ALIGN=MIDDLE  ALT=\"-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B12%2Ahighlight%28%28-x%2B7000%29%29=76400 ALIGN=MIDDLE  ALT=\"8x%2B12%2Ahighlight%28%28-x%2B7000%29%29=76400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B7000 ALIGN=MIDDLE  ALT=\"y=-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the second equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B7000 ALIGN=MIDDLE  ALT=\"-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B%2812%29%28-1%29x%2B%2812%29%287000%29=76400 ALIGN=MIDDLE  ALT=\"8x%2B%2812%29%28-1%29x%2B%2812%29%287000%29=76400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B7000 ALIGN=MIDDLE  ALT=\"-x%2B7000\"   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=8x-12x%2B84000=76400 ALIGN=MIDDLE  ALT=\"8x-12x%2B84000=76400\"   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=-4x%2B84000=76400 ALIGN=MIDDLE  ALT=\"-4x%2B84000=76400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x=76400-84000 ALIGN=MIDDLE  ALT=\"-4x=76400-84000\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 84000 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x=-7600 ALIGN=MIDDLE  ALT=\"-4x=-7600\"   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=%28-7600%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x=%28-7600%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1900 ALIGN=MIDDLE  ALT=\"x=1900\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So this means that Mike invested $1,900 at 8%\r<BR>\n" );
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document.write( "-----------------------------\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1900 ALIGN=MIDDLE  ALT=\"x=1900\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B7000 ALIGN=MIDDLE  ALT=\"y=-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved 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 first equation).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B7000 ALIGN=MIDDLE  ALT=\"y=-x%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281900%29%2B7000 ALIGN=MIDDLE  ALT=\"y=-%281900%29%2B7000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1900 ALIGN=MIDDLE  ALT=\"x=1900\"   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=5100 ALIGN=MIDDLE  ALT=\"y=5100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms \r<BR>\n" );
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document.write( "So Mike invested $5,100 at 12%\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So Mike invested $1,900 at 8% and $5,100 at 12% </SPAN>\n" );
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