A rectangular law whose perimeter is 310 feet is fenced along 3 sides and expensive fencing along the lot cost $20 per foot and inexpensive fencing along with the 2 sides with costs only $4 per foot. The total cost of fencing along the three sides comes 22 thousand two hundred and sixty dollars
Question
Answer:
Sure, I can help you with that.
Let's say the dimensions of the rectangular lot are x and y.
The perimeter of the lot is 310 feet, so 2x + 2y = 310.
We know that the total cost of fencing along the three sides is $22,260, and that the expensive fencing costs $20 per foot and the inexpensive fencing costs $4 per foot.
Let's say that the length of the expensive fencing is a, and the length of the inexpensive fencing is b.
We know that a + b = 2x, and that 20a + 4b = 22,260.
Substituting the first equation into the second equation, we get 20a + 4(2x - a) = 22,260.
Simplifying the equation, we get 16a = 22,260 + 8x.
Dividing both sides of the equation by 16, we get a = 1,403.75 + 0.5x.
Since 2x + 2y = 310, we know that x + y = 155.
Substituting the value of a into this equation, we get x + 1403.75 + 0.5x = 155.
Simplifying the equation, we get 1.5x = 15.25.
Dividing both sides of the equation by 1.5, we get x = 10.17.
Substituting this value of x into the equation a = 1,403.75 + 0.5x, we get a = 1,546.09.
Therefore, the length of the expensive fencing is 1,546.09 feet, and the length of the inexpensive fencing is 10.17 feet.
The total cost of the expensive fencing is 1,546.09 * $20 = $30,921.80.
The total cost of the inexpensive fencing is 10.17 * $4 = $40.68.
The total cost of the fencing is $30,921.80 + $40.68 = $30,962.48.
So the answer is 30962.48
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