SOLUTION: A rectangular plot of ground is to be enclosed by a fence and then divided down the middle by another fence. The fence down the middle costs Php40.00 per running foot and the other

Question 1167808: A rectangular plot of ground is to be enclosed by a fence and then divided down the middle by another fence. The fence down the middle costs Php40.00 per running foot and the other costs Php100.00 and Php 38 400 worth of fencing materials to be used. let x felt be the length of the fence down the middle: express the number of square feet in the area of the plot as a function of x.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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A rectangular plot of ground is to be enclosed by a fence and then divided down the middle by another fence.
The fence down the middle costs Php40.00 per running foot and the other costs Php100.00
and Php 38 400 worth of fencing materials to be used.
Let x felt be the length of the fence down the middle:
express the number of square feet in the area of the plot as a function of x.
~~~~~~~~~~~~~~~~~~~~~~~

Let x be the length of the plot (in feet);
let y be the width of the plot.


We have the x + y + x + y = 2x + 2y feet of the fence at Php 100 per foot
and y feet of the fence at Php 40 per foot.


Write the cost equation for the fence

    100*(2x+2y) + 40y = 38400  Php.


Simplify and express y

    200x + 200y + 40y = 38400

    200x + 240y = 38400

    y = 160 -  = 160 - .


Now the area of the plot is

    area = xy = x*(160 -  = 160x - .


It is the desired expression of the area of the plot via x.

Solved.

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