A rancher has 1600 feet of fencing to enclose a rectangular pig pen. However, one side of the pen lies along a river and requires no fencing. Express the area of the pen, A, as a function of x.

Step-by-step explanation:

Let the dimensions of the pen be x and y.

Area, A = xy

Let y be the side oppossite the river, therefore:

The perimeter of the pen = 2x+y

Since the rancher has 1600 feet of fencing to enclose the pen.

2x+y=1600

We make y the subject of the formula

y=2x-1600

Substitute y=2x-1600 into the area function

A = x(2x-1600)

The area of the pen as a function of x is therefore:

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