Need help

sgadipat 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, what is the total length of the fence in feet?

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

Can some one solve this and explain the solution please?

The total length of the pickets will be given by the length of one picket times the number of pickets that you have. This means x pickets times 1/2 inches per picket, or:

x/2

Now, think about this: if you have 5 pickets, you have 4 spaces between them. If you have 6 pickets, you have 5 spaces between them. If you have 7 pickets, you have 6 spaces between them. And so on, and so forth.

So if you have x pickets, you have x - 1 spaces between them. The length of each space times the number of spaces will give you the total length of all the spaces combined. This means 6 inches times x - 1 spaces, or:

6(x - 1)

Then we add the total length of the pickets to the total length of the spaces to find the total combined length of eveything:

6(x - 1) + x/2
6x - 6 + x/2
(12x/)- 6 + x/2
(13x/2) - 6

Answer B is correct!

sgadipat 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, what is the total length of the fence in feet?

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

Can some one solve this and explain the solution please?

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 we 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.

It should be E. Its looking for feet instead of inches.