SOLUTION: A rectangular lot whose perimeter is 270 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 24 per foot. An inexpensive fencing along the two

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Question 1122733: A rectangular lot whose perimeter is 270 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 24 per foot. An inexpensive fencing along the two side widths costs only $ 4 per foot. The total cost of the fencing along the three sides comes to $ 2280. What are the​ lot's dimensions?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Helps to draw this
width=x
length is 270-2x
2x*4=width cost or 8x
24(270-2x)=length cost or 6480-48x
total is -40x+6480=2280
-40x=-4200
x=105 feet width, 2 of them, cost is $840
270-2x is 60 feet length, cost is $1440
Total cost is $2280



Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Let W be the width, in feet.


Then the length is  (135-W) ft.


The money equation is


4*(2W) + 24*(135-W) = 2280.


Simplify and solve for W:


8W + 24*135 - 24W = 2280

24*135 - 2280 = 24W - 8W 

960 = 16W  ====>  W =  = 60.


Anwer.  The width is 60 ft;  the length is 135-60 = 75 ft.


Check.  Perimeter = 2*(60 + 75) = 270 ft.             ! Correct ! 

        The cost = 4*(2*60) + 24*75 = 2280 dollars.   ! Correct !

Solved.

===============

Be aware !   The solution by  @Boreal  is incorrect.


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