I want to fence in a square vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. Find the total cost of the fencing as a function of the length of a side x.
total for east and west sides = 2 s*4 = 8 s
total for North and South sides = 2 s * 2 = 4 s
so total = $ 12 s
check ===> yes averaged out to $3 per foot :)
To find the total cost of the fencing, we need to consider the cost of each side and then add them up.
Let's start with the east and west sides. Since the fence for these sides costs $4 per foot, the total length of the east and west sides combined is 2x (since there are two sides). So the cost of these sides is 2x * $4 = $8x.
Now let's move on to the north and south sides. The fence for these sides costs $2 per foot, and since they are opposite sides, their total length is also 2x. So the cost of these sides is 2x * $2 = $4x.
To find the total cost of the fencing, we add up the costs of all the sides. Therefore, the total cost C(x) as a function of the length of a side x is given by:
C(x) = $8x (east and west sides) + $4x (north and south sides)
= $12x
So, the total cost of the fencing is $12x.