A rectangular lot whose perimeter is 260 ft is fenced along three sides. An expensive fencing along the lot's length cost $ 36 per foot. An inexpensive fencing along the two side widths costs only $ 6 per foot. The total cost of the fencing along the three sides comes to $ 3600. What are the lot's dimensions?
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To solve this problem, we need to set up and solve a system of equations based on the given information.
Let's assume the length of the rectangular lot is "L" ft and the width is "W" ft.
Given that the perimeter of the lot is 260 ft, we can write the equation:
2L + W = 260 ft (equation 1)
Also, given that the expensive fencing along the length costs $36 per foot and the inexpensive fencing along the two widths costs $6 per foot, and the total cost of the fencing along the three sides is $3600, we can write the equation:
36L + 6W = 3600 (equation 2)
Now, we have a system of equations consisting of equation 1 and equation 2. We can solve this system to find the values of L and W.
First, let's simplify equation 1 by dividing both sides by 2:
L + 0.5W = 130 (equation 3)
Now, we have equations 3 and 2. Let's solve this system using the substitution method.
From equation 3, we can express L in terms of W:
L = 130 - 0.5W (equation 4)
Substitute equation 4 into equation 2:
36(130 - 0.5W) + 6W = 3600
Simplify and solve for W:
4680 - 18W + 6W = 3600
4680 - 12W = 3600
-12W = 3600 - 4680
-12W = -1080
W = (-1080) / (-12)
W = 90 ft
Now substitute the value of W into equation 4 to find L:
L = 130 - 0.5W
L = 130 - 0.5(90)
L = 130 - 45
L = 85 ft
Therefore, the dimensions of the rectangular lot are 85 ft (length) and 90 ft (width).