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