document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6611>Question 6611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir/Madam, <BR>\n" );
document.write( "I am confronted with the following problem:\r<BR>\n" );
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document.write( "\"A box with an open top is to be constructed by cutting 3-in squares from the corners of a rectangular sheet of tin, whose length is twice its width, and then folding up the sides. What size sheet of tin will produce a box having a volume of 60 cubic inches?\"\r<BR>\n" );
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document.write( "I did the following:\r<BR>\n" );
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document.write( "1) Volume = l * w * h<BR>\n" );
document.write( "l = 2w<BR>\n" );
document.write( "h = 3<BR>\n" );
document.write( "2) 60 = 2w * w * 3<BR>\n" );
document.write( "3) 6w^2 = 60<BR>\n" );
document.write( "4) w^2 = 10<BR>\n" );
document.write( "5) w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%2810%29+ ALIGN=MIDDLE  ALT=\"+sqrt%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But that is not correct. The right answer for the width is 8 inches. What did I do wrong?<BR>\n" );
document.write( "Thanks in advance.<BR>\n" );
document.write( "Regards,<BR>\n" );
document.write( "-Mike </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3594 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=3594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alright. We're cool with V = l * w * h, right, and we know that h = 3 and the volume is 60 in^2. So far we've got\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+=+l+%2A+w+%2A+3+ ALIGN=MIDDLE  ALT=\"+60+=+l+%2A+w+%2A+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The trick is with the L and the W. You were right when you said that L = 2W. The length of the original sheet is twice the width of the original sheet BEFORE chopping of 3-inch by 3-inch squares on all four corners. When you chop off square corners, the actual length and width of the resulting folded box will definitely be shorter than the original L and W you started with.\r<BR>\n" );
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document.write( "Let's take the width. We decided to call it w. Now, when we cut off 3 inches from all 4 corners, that would actually chop 6 inches off the width. So the width of your box will have to be w - 6.\r<BR>\n" );
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document.write( "We know that the length = 2w BEFORE cutting off squares. Like the width, 3 inches were also chopped off the length from BOTH sides, making the actual length (of your box) 6 inches shorter. So the length of the box will be 2w - 6.\r<BR>\n" );
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document.write( "Let's now plug in the box's width and length:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+=+%282w+-+6%29%28w+-+6%29%283%29+ ALIGN=MIDDLE  ALT=\"+60+=+%282w+-+6%29%28w+-+6%29%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- We'll solve for the width eventually.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+=+%282w+-+6%29%28w+-+6%29+ ALIGN=MIDDLE  ALT=\"+20+=+%282w+-+6%29%28w+-+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Divided both sides by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+=+2w%5E2+-+18x+%2B+36+ ALIGN=MIDDLE  ALT=\"+20+=+2w%5E2+-+18x+%2B+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Performed \"FOIL\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+2w%5E2+-+18x+%2B+16+ ALIGN=MIDDLE  ALT=\"+0+=+2w%5E2+-+18x+%2B+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Subtract 20 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+w%5E2+-+9x+%2B+8+ ALIGN=MIDDLE  ALT=\"+0+=+w%5E2+-+9x+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%28w+-+8%29%28w+-+1%29+ ALIGN=MIDDLE  ALT=\"+0+=+%28w+-+8%29%28w+-+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- \"UnFOILED\" or factored\r<BR>\n" );
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document.write( "Just by looking at the above equation, the width is either 8 or 1. We'll have to throw out the 1 because that measure for the width won't work if you'll have to chop 6 inches off it. The 8 would, though. If 8 is the width, and the length is twice the width, then the length is 16. So you've got a sheet that was 16\" x 8\". </SPAN>\n" );
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