document.write( "Question 66863: A woman has a flower bed measuring 9 feet by 5 feet in her backyard. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 square feet for the border, how wide can the border be? \n" ); document.write( "
Algebra.Com's Answer #47548 by ptaylor(2198)![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "I AM ASSUMING THAT THE BORDER IS INSIDE THE 9X5 FLOWER BED.\r \n" ); document.write( "\n" ); document.write( "Let x= the width of the border \n" ); document.write( "Area of the flower bed plus border =9*5=45 sq ft\r \n" ); document.write( "\n" ); document.write( "Length of the flower bed less the border is 9-2x \n" ); document.write( "Width of the flower bed less the border is 5-2x \n" ); document.write( "Area of flower bed less the border is (9-2x)(5-2x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So our equation is:\r \n" ); document.write( "\n" ); document.write( "45-(9-2x)(5-2x)=24 multiplying out \n" ); document.write( "45-45+28x-4x^2=24 subtract 24 from both sides and multiply by -1 \n" ); document.write( "4x^2-28x+24=0 divide by 4 \n" ); document.write( "x^2-7x+6=0 It can be factored:\r \n" ); document.write( "\n" ); document.write( "(x-6)(x-1)=0\r \n" ); document.write( "\n" ); document.write( "x=6 ft width of border \n" ); document.write( "or \n" ); document.write( "x=1 ft width of border\r \n" ); document.write( "\n" ); document.write( "CK\r \n" ); document.write( "\n" ); document.write( "border is 6 ft----Length, less border, is 9-2x=9-12=-3 \r \n" ); document.write( "\n" ); document.write( "DOESN'T WORK GIVES NEGATIVE LENGTHS\r \n" ); document.write( "\n" ); document.write( "Border is 1 ft----Length,less border, is 9-2=7 ft \n" ); document.write( "Width, less border, is 5-2-------------3 ft\r \n" ); document.write( "\n" ); document.write( "Area, less border, is 3*7=21 sq ft \n" ); document.write( "Area of border 45 sq ft -21 sq ft =24 sq ft \r \n" ); document.write( "\n" ); document.write( "Hope this helps ----ptaylor\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |