document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60963>Question 60963</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534400329/algebrahomeworkh>Algebra for College Students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original 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 #41915 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=41915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the width of the original piece of cardboard.  Then its length is x+2<BR>\n" );
document.write( "If you were to cut out 2-unit squares from each corner and then fold up the flaps to create an open box, the width of the open box would be (x-4) and its length would be ((x+2)-4), and its height would, of course, be 2.<BR>\n" );
document.write( "Now you can write the equation for the volume of the box as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28x-4%29%28%28x%2B2%29-4%29%282%29 ALIGN=MIDDLE  ALT=\"V+=+%28x-4%29%28%28x%2B2%29-4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > But the volume is given as 70 cubic units, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28%28x%2B2%29-4%29%282%29+=+70 ALIGN=MIDDLE  ALT=\"%28x-4%29%28%28x%2B2%29-4%29%282%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28x-2%29%282%29+=+70 ALIGN=MIDDLE  ALT=\"%28x-4%29%28x-2%29%282%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-6x%2B8%29%282%29+=+70 ALIGN=MIDDLE  ALT=\"%28x%5E2-6x%2B8%29%282%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B8+=+35 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B8+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 35 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x-27+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-6x-27+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve this quadratic equation for x by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Applying the zero product principle, you get:<BR>\n" );
document.write( "x = -3 Discard this solution as the width can't be a negative value.<BR>\n" );
document.write( "x = 9 This is the width of the original piece of cardboard.<BR>\n" );
document.write( "x+2 = 11 This is the length of the original piece of cardboard.\r<BR>\n" );
document.write( "\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "V = (9-4)(11-4)(2) = (5)(7)(2) = 70<BR>\n" );
document.write( "  </SPAN>\n" );
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