A fence consists of m lengths of fence that are each n feet

AAPL wrote:A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length of the fence including the fence posts on each end?

A. mn
B. m(n + x)
C. m(n + x) + x
D. m(n +x) + 2x
E. 2mn

The total length of the fence only (without the posts) is mn feet long. Since each post is x feet long and there is a post at each end of the fence in addition to the posts separating each length of the fence, there must be (m + 1) posts along the fence. Thus the total length of the posts is x(m + 1), and the total length of the fence, including the posts, is:

mn + x(m + 1)

mn + xm + x

m(n + x) + x

Alternate Solution:

Let’s suppose that there were m = 3 lengths of fence that are n = 2 feet long and the posts separating the fences were x = 1 foot. Under these assumptions, the total length is 1 + 2 + 1 + 2 + 1 + 2 + 1 = 10 feet. Let us see which answer choice(s) give us 10 when m = 3, n = 2 and x = 1:

Answer Choice A:

mn = 3(2) = 6

Eliminate answer choice A.

Answer Choice B:

m(n + x) = 3(2 + 1) = 9

Eliminate answer choice B.

Answer Choice C:

m(n + x) + x = 3(2 + 1) + 1 = 10

C is a possible choice.

Answer Choice D:

m(n + x) + 2x = 3(2 + 1) + 2 = 11

Eliminate answer choice D.

Answer Choice E:

2mn = 2(3)(2) = 12

Eliminate answer choice E.

The only possible answer choice is C.

Answer: C