document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849981>Question 849981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangular piece of cardboard is 945 square inches. The cardboard is used to make an open box by cutting 3-inch squares from each corner and turning up the sides. If the box is to have a volume of 1755 cubic inches, find the dimensions.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511874 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=511874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "x and y, the dimensions.  Uncut cardboard.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=945 ALIGN=MIDDLE  ALT=\"xy=945\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Cutting off corners 3 by 3 square inches.<BR>\n" );
document.write( "Base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%2A3%29%28y-2%2A3%29 ALIGN=MIDDLE  ALT=\"%28x-2%2A3%29%28y-2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Height is simply 3.\r<BR>\n" );
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document.write( "VOLUME is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-6%29%28y-6%29=1755 ALIGN=MIDDLE  ALT=\"3%28x-6%29%28y-6%29=1755\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This volume equation can be a little bit more simplified initially:<BR>\n" );
document.write( "Volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28y-6%29=585 ALIGN=MIDDLE  ALT=\"%28x-6%29%28y-6%29=585\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let me leave this unfinished.  The two equations to use are the system:<BR>\n" );
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document.write( "xy=945<BR>\n" );
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document.write( "(x-6)(y-6)=585<BR>\n" );
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document.write( "The second equation, the volume one gives <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-6x-6y%2B36=585 ALIGN=MIDDLE  ALT=\"xy-6x-6y%2B36=585\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And substituting for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=945 ALIGN=MIDDLE  ALT=\"xy=945\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get after a simplification,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-6y%2B396=0 ALIGN=MIDDLE  ALT=\"-6x-6y%2B396=0\"   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-66=0 ALIGN=MIDDLE  ALT=\"x%2By-66=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again substituting from the area as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=945%2Fx ALIGN=MIDDLE  ALT=\"y=945%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, obtain<BR>\n" );
document.write( "after further steps,<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E2-66x%2B945=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E2-66x%2B945=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using the general solution to a quadratic equation gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2866%2Bsqrt%28576%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2866%2Bsqrt%28576%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=45%29 ALIGN=MIDDLE  ALT=\"highlight%28x=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (we use the positive square root).<BR>\n" );
document.write( "From this and the area equation again, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=21%29 ALIGN=MIDDLE  ALT=\"highlight%28y=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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