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A product packaging firm manufactures cardboard trays for holding 24 12 oz cans.
\n" ); document.write( " The process begins with a rectangular piece of cardboard that is 5 inches longer than it wide.
\n" ); document.write( " 2 inch squares are cut from each corner, and the flaps are folded up to form a tray.
\n" ); document.write( " if the area of the bottom of the tray is 176 square inches, what are the original dimensions of the rectangle piece of cardboard.
\n" ); document.write( ":
\n" ); document.write( "Let w = the width of the cardboard
\n" ); document.write( "then
\n" ); document.write( "(w+5) = the length
\n" ); document.write( ":
\n" ); document.write( "2 in squares are cut from each corner, therefore each dimension is reduced by 4 in.
\n" ); document.write( "(w-4) = the width of the box
\n" ); document.write( "(w+1) = the length of the box
\n" ); document.write( ";
\n" ); document.write( "the area of the bottom
\n" ); document.write( "(w-4)(w+1) = 176
\n" ); document.write( "FOIL
\n" ); document.write( "w^2 + w - 4w - 4 = 176
\n" ); document.write( "w^2 + w - 4w - 4 - 176 = 0
\n" ); document.write( "w^2 - 3w - 180 = 0
\n" ); document.write( "You can use the quadratic formula a=1; b=-3; c=-180, but this will factor to:
\n" ); document.write( "(w-15)(w+12) = 0
\n" ); document.write( "The positive solution is what we want here
\n" ); document.write( "w = 15 in is the original width of the card board
\n" ); document.write( "then
\n" ); document.write( "15+5 = 20 in is the original length
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this by finding the area of the bottom using these dimensions
\n" ); document.write( "Subtract 4 from each cardboard dimension
\n" ); document.write( "11 * 16 = 176 \n" ); document.write( "