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.
