document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191762>Question 191762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm kate and I need some help with linear systems. <BR>\n" );
document.write( "Snookers Lumber can convert logs into either lumber or plywood. In a given day the mill turns out twice as many units of plywood as lumber. The mill makes a profit of $30 a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12480. Thank-you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143870 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=143870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=# of plywood boards, y=# of lumber \r<BR>\n" );
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document.write( "\"In a given day, the mill turns out twice as many units of plywood as lumber\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\"It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood.  How many of each unit must be produced and sold in order to make a profit of $12480\" translates to: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45x%2B30y=12480 ALIGN=MIDDLE  ALT=\"45x%2B30y=12480\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the following system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45x%2B30y=12480 ALIGN=MIDDLE  ALT=\"45x%2B30y=12480\"   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=45%282y%29%2B30y=12480 ALIGN=MIDDLE  ALT=\"45%282y%29%2B30y=12480\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y ALIGN=MIDDLE  ALT=\"2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=90y%2B30y=12480 ALIGN=MIDDLE  ALT=\"90y%2B30y=12480\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120y=12480 ALIGN=MIDDLE  ALT=\"120y=12480\"   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=y=%2812480%29%2F%28120%29 ALIGN=MIDDLE  ALT=\"y=%2812480%29%2F%28120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 120 to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=104 ALIGN=MIDDLE  ALT=\"y=104\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=104 ALIGN=MIDDLE  ALT=\"y=104\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <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=2%28104%29 ALIGN=MIDDLE  ALT=\"x=2%28104%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104 ALIGN=MIDDLE  ALT=\"104\"   DISABLED_style= \"max-width:90%; height:auto;\" > for 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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=208 ALIGN=MIDDLE  ALT=\"x=208\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\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=208 ALIGN=MIDDLE  ALT=\"x=208\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=104 ALIGN=MIDDLE  ALT=\"y=104\"   DISABLED_style= \"max-width:90%; height:auto;\" > which the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(202,101\right)\">\r<BR>\n" );
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document.write( "This means that they must sell 208 units of plywood and 104 units of lumber to obtain a profit of $12,480 </SPAN>\n" );
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