document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632571>Question 632571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a piece of cardboard, twice as long as it is wide. I will cut 4x4 squares out of each corner, so i fold up the corners and use it as a tray. The volume of the tray will be 96 cubic inches. How large is the piece of cardboard? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398466 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a piece of cardboard, twice as long as it is wide.<BR>\n" );
document.write( " I will cut 4x4 squares out of each corner, so i fold up the corners and<BR>\n" );
document.write( " use it as a tray. <BR>\n" );
document.write( "The volume of the tray will be 96 cubic inches. <BR>\n" );
document.write( "How large is the piece of cardboard?<BR>\n" );
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document.write( "let x = the width of the cardboard<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2x = the length of the cardboard<BR>\n" );
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document.write( "The dimensions of the tray<BR>\n" );
document.write( "the 4\" squares will reduce both dimensions of the cardboard by 8\"<BR>\n" );
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document.write( "(x-8) = the width of the tray<BR>\n" );
document.write( "(2x-8) = the length of the tray<BR>\n" );
document.write( "4 inches = the height of the tray<BR>\n" );
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document.write( "The volume of the tray, Length * Width * height = 96 cu/in<BR>\n" );
document.write( "(2x-8)*(x-8)*4 = 96<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "4(2x^2 - 16x - 8x + 64) = 96<BR>\n" );
document.write( "4(2x^2 - 24x + 64) = 96<BR>\n" );
document.write( "8x^2 - 96x + 256 = 96<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "8x^2 - 96x + 256 - 96 = 0<BR>\n" );
document.write( "8x^2 - 96x + 160 = 0<BR>\n" );
document.write( "simplify, divide by 8<BR>\n" );
document.write( "x^2 - 12x + 20 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-2)(x-10) = 0<BR>\n" );
document.write( "Two solutions but only one will make sense<BR>\n" );
document.write( "x = 10 inches is the  width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "20 inches is the length<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The original cardboard is 20 by 10<BR>\n" );
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document.write( "Check this by finding the volume<BR>\n" );
document.write( "(20-8)*(10-8)*4 = 96 </SPAN>\n" );
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