document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=708445>Question 708445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this word problem:  A large plywood box has a volume of 72 ft3. Its length is 9 ft greater than its height, and its width is 1 ft less than its height. What are the dimensions of the box?\r<BR>\n" );
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document.write( "What does x equal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436152 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=436152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A large plywood box has a volume of 72 ft3. <BR>\n" );
document.write( "Its length is 9 ft greater than its height, and its width is 1 ft less than its height.<BR>\n" );
document.write( " What are the dimensions of the box?<BR>\n" );
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document.write( "let x = the height<BR>\n" );
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document.write( "\"Its length is 9 ft greater than its height,\"<BR>\n" );
document.write( "L = (x+9)<BR>\n" );
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document.write( "its width is 1 ft less than its height.\"<BR>\n" );
document.write( "W = (x-1)<BR>\n" );
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document.write( "L * W * H = 72<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "(x+9)*(x-1)*x = 72<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "(x^2 - x + 9x -9 )*x = 72<BR>\n" );
document.write( "Which is<BR>\n" );
document.write( "x^3 + 8x^2 - 9x - 72 = 0<BR>\n" );
document.write( "We can group factor here<BR>\n" );
document.write( "x^2(x+8) - 9(x+8) = 0<BR>\n" );
document.write( "Factor out (x+8)<BR>\n" );
document.write( "(x+8)(x^2-9) = 0<BR>\n" );
document.write( "three solutions<BR>\n" );
document.write( "x = -8<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x^2 = 9<BR>\n" );
document.write( "x = +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = -3<BR>\n" );
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document.write( "IN the real world of boxes only the positive solution will be valid<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "then the box dimensions:<BR>\n" );
document.write( "3 + 9 = 12 is the length<BR>\n" );
document.write( "3 - 1 = 2 is the width<BR>\n" );
document.write( "3 = the height<BR>\n" );
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document.write( "See if that flies: 12 * 2 * 3 = 72<BR>\n" );
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