document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162853>Question 162853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a company plans to lay off 10% of its employees in its aerospace division and 15% of its employees in its agricultural divsion. If altogether 12% of the 3000 employees in these two division will be laid off, then how many employees are in each divsion.\r<BR>\n" );
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document.write( "Heres what I've tried:  .10 (x)  + .15(x) +.12 = 3000<BR>\n" );
document.write( "                          300        450<BR>\n" );
document.write( "                         .12x  =  3000<BR>\n" );
document.write( "                          ____     ____<BR>\n" );
document.write( "                          .12       .12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120021 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=120021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=# of aerospace employees and y=# of agricultural employees\r<BR>\n" );
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document.write( "From the problem, we know that there are a total of 3,000 employees from both divisions. So this means that the sum of the two groups will be 3,000. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=3000 ALIGN=MIDDLE  ALT=\"x%2By=3000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, since 12% of the total workers will be laid off, this means that 0.12(3000)=360 employees will be laid of in total in these two divisions. So the sum of the layoffs in the aerospace division (which is 10% of \"x\" and is represented by 0.10x) and the layoffs in the aerospace division (which is 15% of \"y\" and is represented by 0.15y) will equal 360. This translates to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10x%2B0.12y=360 ALIGN=MIDDLE  ALT=\"0.10x%2B0.12y=360\"   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=0.10x%2B0.15y=360 ALIGN=MIDDLE  ALT=\"0.10x%2B0.15y=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B15y=36000 ALIGN=MIDDLE  ALT=\"10x%2B15y=36000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by 100 to make every number a whole number. Note: this will move the decimal point two spots to the right.\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=3000%2C10x%2B15y=36000%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=3000%2C10x%2B15y=36000%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=-10%28x%2By%29=-10%283000%29 ALIGN=MIDDLE  ALT=\"-10%28x%2By%29=-10%283000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -10.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x-10y=-30000 ALIGN=MIDDLE  ALT=\"-10x-10y=-30000\"   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%28-10x-10y=-30000%2C10x%2B15y=36000%29 ALIGN=MIDDLE  ALT=\"system%28-10x-10y=-30000%2C10x%2B15y=36000%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=%28-10x-10y%29%2B%2810x%2B15y%29=%28-30000%29%2B%2836000%29 ALIGN=MIDDLE  ALT=\"%28-10x-10y%29%2B%2810x%2B15y%29=%28-30000%29%2B%2836000%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=%28-10x%2B10x%29%2B%28-10y%2B15y%29=-30000%2B36000 ALIGN=MIDDLE  ALT=\"%28-10x%2B10x%29%2B%28-10y%2B15y%29=-30000%2B36000\"   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%2B5y=6000 ALIGN=MIDDLE  ALT=\"0x%2B5y=6000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the x terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=6000 ALIGN=MIDDLE  ALT=\"5y=6000\"   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=%286000%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%286000%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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=1200 ALIGN=MIDDLE  ALT=\"y=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x-10y=-30000 ALIGN=MIDDLE  ALT=\"-10x-10y=-30000\"   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=-10x-10%281200%29=-30000 ALIGN=MIDDLE  ALT=\"-10x-10%281200%29=-30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1200 ALIGN=MIDDLE  ALT=\"y=1200\"   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=-10x-12000=-30000 ALIGN=MIDDLE  ALT=\"-10x-12000=-30000\"   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=-10x=-30000%2B12000 ALIGN=MIDDLE  ALT=\"-10x=-30000%2B12000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12000 ALIGN=MIDDLE  ALT=\"12000\"   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=-10x=-18000 ALIGN=MIDDLE  ALT=\"-10x=-18000\"   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=%28-18000%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x=%28-18000%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10 ALIGN=MIDDLE  ALT=\"-10\"   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=1800 ALIGN=MIDDLE  ALT=\"x=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1800 ALIGN=MIDDLE  ALT=\"x=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1200 ALIGN=MIDDLE  ALT=\"y=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that there are 1,800 aerospace employees and 1,200 agricultural employees (before the layoffs).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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