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A rectangular piece of cardboard that is 3 feet longer than it is wide will be
\n" ); document.write( " made into an open-topped box by cutting 2 ft squares out of each corner and folding up the sides.
\n" ); document.write( "The volume of the resulting box will be 140 cubic feet.
\n" ); document.write( " Find the original dimensions of the cardboard.
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\n" ); document.write( "Let x = the width of the piece of cardboard
\n" ); document.write( "then
\n" ); document.write( "(x+3) = the length of the cardboard
\n" ); document.write( ":
\n" ); document.write( "Cutting 2 ft squares out of each corner will give the box dimensions
\n" ); document.write( "(x+3-4) by (x-4) by 2 ft
\n" ); document.write( "which is:
\n" ); document.write( "(x-1) by (x-4) by 2
\n" ); document.write( ":
\n" ); document.write( "The volume
\n" ); document.write( "2*(x-1)*(x-4) = 140
\n" ); document.write( "FOIL
\n" ); document.write( "2*(x^2 - 4x - x + 4) = 140
\n" ); document.write( "2*(x^2 - 5x + 4) = 140
\n" ); document.write( "2x^2 - 10x + 8 - 140 = 0
\n" ); document.write( "2x^2 - 10x - 132 = 0
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "x^2 - 5x - 66 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-11)(x+6) = 0
\n" ); document.write( "positive solution is what we want here
\n" ); document.write( "x = 11 ft is the width of the cardboard
\n" ); document.write( "then
\n" ); document.write( "11 + 3 = 14 ft is the length
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding the vol of the box
\n" ); document.write( "(14-4)*(11-4)* 2 =
\n" ); document.write( "10 * 7 * 2 = 140
\n" ); document.write( " \n" ); document.write( "