SOLUTION: A livestock pen is built in the shape of a rectangle that is twice as long as it is wide. The perimeter is 48 feet. If the material used to build the pen is $1.25 per foot for the

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Question 902541: A livestock pen is built in the shape of a rectangle that is twice as long as it is wide. The perimeter is 48 feet. If the material used to build the pen is $1.25 per foot for the longer sides and $3.25 per foot for the shorter sides, find the cost to build the pen.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for the perimeter of a rectangle is P = 2L + 2W.
Equation 1: 48+=+2L+%2B+2W
Equation 2: L+=+2W
Plug 2W into equation 1 for L.
48+=+2%2A%282W%29+%2B+2W
Multiply the 2 through.
48+=+4W+%2B+2W
Combine like terms.
48+=+6W
Divide both sides by 6.
highlight%288+=+W%29
Now plug 8 into equation 2 for W and solve for L.
Equation 2: L+=+2W
L+=+2%2A%288%29
highlight_green%28L+=+16%29
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Now it is time to calculate the cost of the fence.
The longer side costs $1.25/ft.
Multiply $1.25/ft by the Length of 16ft. Multiply that by 2 because there are two sides of the rectangle.
$1.25 * 16 * 2 = $40 for the long sides.
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The short side costs $3.25/ft.
Multiply $3.25/ft by the Length of 8ft. Multiply that by 2 because there are two sides of the rectangle.
$3.25 * 8 * 2 = $52 for the long sides.
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Now add the costs together.
$40 + $52 = $92
It will cost $92 to build the pen.