Question

Paul is building a rectangular pen for his goat. The length of the pen will be 5feet more than twice as long as the width of the pen. The cost of the pen will be $7.50 per foot of fencing. If x represents the width of the oen, c(x) in terms of c to represent the cost of the fencing if x represents the width the pen, write a function

Answer 1

Answer:

$C(x) = 45x + 75\\\text{where x is the width of rectangular pen}$

Step-by-step explanation:

We are given the following in the question:

The length of the pen will be 5 feet more than twice as long as the width of the pen.

Let y be the length and x be the width. Thus, we can write:

$y = 2x +5$

Fencing = Perimeter of rectangular pen

$\text{Perimeter of rectangle} = 2(\text{length} + \text{width})\\ P = 2(y+x)\\P=2(2x+5+x)\\P= 2(3x+5)\\P = (6x + 10)\text{ feet}$

The cost of the pen will be $7.50 per foot of fencing.

Total Cost of fencing =

$\text{Cost of fencing}\times \text{Perimeter}\\C(x) = 7.50\times (6x+10)\\C(x) = 45x + 75\\\text{where x is the width of rectangular pen}$

is the required cost function.