Question

Can some one please explain this to me in the simplest possible language?
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)

A. 17
B. 28
C. 35
D. 39
E. 50

Answer 1

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Answer 2

to work out the total length :of 6 posts and 5 chains:= 6 * 0.5 = 3 ft this is the length of the 6 posts
and we have 5 chains at 5 feet loing - total length %*5 = 25 ft

This is a total length of 25 + 3 = 28 ft. So B could be a total length

We can work out a formula for working out the length of a fence
and that is

L = 0.5x + 5y
where x = number of posts and y = number of chains
(0.5 ft and 5 ft)
but we know that there must be 1 less chain than posts as there must be a post at each end.
so y = x-1
And our formula becomes

L = 0.5 x + 5(x-1)
L = 5.5x - 5 - THats our formula

Now look at the options
28 = 5.5 * 6 - 5 = 33 -5 = 28 so 28 ok

could 17 be the length:

17 = 5.5x - 5
5.5x = 22
x = 4
Yes 17 is Ok

could 35 be length
35 = 5.5x -5
5.5x = 40
x = 40/5.5 = 7.3

THIS IS THEONE WE ARE LOOKING FOR
x (the number of posts) must of course must be a whole number.

So C. 35 cannot be a length.

I assume there is only one of these - you can try the other two to make sure if you like