document.write( "Question 1194614: A property owner wants to fence a garden plot adjacent to a road. The fencing next to the road must be sturdier and costs $5 per foot and the other fencing just $3 per foot. The garden has to have an area of 1200 square feet. Find the garden dimensions that he can fence-in he spends $500.\r
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Algebra.Com's Answer #826859 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Find the garden dimensions that he can fence-in he spends $500.
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document.write( "Let x be the length of the fence parallel to the road.\r\n" );
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document.write( "Then the cost of the two sides of the fence parallel to the road is 5x+3x = 8x dollars,\r\n" );
document.write( "and the cost of the two perpendicular sides is the rest 500-8x dollars.\r\n" );
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document.write( "So the cost of one such side is  (500-8x)/2 = (250-4x)  dollars;\r\n" );
document.write( "hence, the length of the perpendicular side is y = (250-4x)/3 feet.\r\n" );
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document.write( "The area equation is then\r\n" );
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document.write( "    xy = 1200  square feet,  or\r\n" );
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document.write( "     = 1200.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    x*(250-4x) = 3600\r\n" );
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document.write( "    -4x^2 + 250x = 3600\r\n" );
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document.write( "    4x^2 - 250x + 3600 = 0\r\n" );
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document.write( "Using the quadratic formula, you get two possible solutions: x= 40 ft and  x= 22.5 ft.\r\n" );
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document.write( "So, the possible dimensionsd are  x= 40 ft   along the road by 1200/40   = 30     ft in perpendicular direction,  \r\n" );
document.write( "                              or  x =22.5 ft along the road by 1200/22.5 = 53 1/3 ft in perpendicular direction.\r\n" );
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document.write( "CHECK.  (a)  5*40 + 3*40 + 3*(30+30) = 500 dollars                total fence cost;\r\n" );
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document.write( "        (b)  5*22.5 + 3*22.5 + 3*(53 1/3 + 53 1/3) = 500 dollars  total fence cost.    ! Correct !\r\n" );
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