ardz24 wrote:A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?

A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

Let x=2, implying that there are only 2 pickets.
Length of the 2 pickets = 2(1/2) = 1 inch.
The space between them = 6 inches.
Total length = 1+6 = 7 inches.
Total length in feet = 7/12. This is our target.

Now plug x=2 into the answers to see which yields our target of 7/12.

Only E works:
(13x-12)/24 = (13*2 - 12)/24 = 7/12.

The correct answer is E.

A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?

A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

OA: E

Need explanation why E is the correct answer?

Hi ardz24,
Let's take a look at your question.

Since there are x pickets in the fence and each picket is 1/2 inch wide, so width of all x pickets will be (1/2)x
Now, lets find the total gap between x pickets.
If there are only 2 pickets, the gap between them is (2-1)(6) = (1)(6) = 6 inches
If there are 3 pickets, the gap between them is (3-1)(6) = (2)(6) = 12 inches
If there are 4 pickets, the gap between them is (4-1)(6) = (3)(6) = 18 inches
.....
Similarly, If there are x pickets, the gap between them is (x-1)(6) = (6x-6) inches

Total length of the fence in inches= width of x pickets + gap between x pickets
$$=\frac{1}{2}x+\left(6x-6\right)$$
$$=\frac{1}{2}x+\frac{12}{2\ }x-6$$
$$=\frac{13}{2\ }x-6$$

We are asked to find the length of fence in feet.
We know that, 1 foot = 12 inches and 1 inch = 1/12 foot, Therefore,
Total length of the fence in feet =
$$=\frac{1}{12}\left(\frac{13}{2\ }x-6\right)$$
$$=\frac{1}{12}\left(\frac{13x-12}{2\ }\right)$$
$$\left(\frac{13x-12}{24}\right)$$

Therefore, Option E is correct.

I am available, if you'd like any follow up.