Construction of Straight Fence

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

How is this done?

 

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? (12inches = 1 foot)
let make a sketch: p=post, c=chain
p................c.............p...........c..............p......c.........p =>fence begins and ends with a post
6in 5ft

5ft=5*12in=60in
possible lengths:
6in +60in +6in =72in or (72/12)ft=6ft
6in +60in +6in +60in +6in=138in or 11.5 ft
6in +60in +6in +60in +6in +60in +6in=204in or 17ft
6in +60in +6in +60in +6in +60in +6in+60in +6in =270in or 22.5ft
6in +60in +6in +60in +6in +60in +6in+60in +6in+60in +6in=336in or 28ft
6in +60in +6in +60in +6in +60in +6in+60in +6in+60in +6in+60in +6in=402in or 33.5ft
6in +60in +6in +60in +6in +60in +6in+60in +6in+60in +6in+60in +6in+60in +6in=468in or 39ft
6in +60in +6in +60in +6in +60in +6in+60in +6in+60in +6in+60in +6in+60in +6in+60in +6in=534in or 44.5ft
6in +60in +6in +60in +6in +60in +6in+60in +6in+60in +6in+60in +6in+60in +6in+60in +6in+60in +6in=600in or 50ft


C. 35->could not be the length of the fence in feet

 

One thing is for sure, on any given test, I would surely take a wild guess. Back in my student days, I always guessed choice C. So, I would be right by selecting C but simply based on a guess.

I really tried to understand this fence problem but did not even come close. Looking at all the work you did, I don't feel so bad. Look for miscellaneous word problems here.

 

If this fence has "n" sections (n+ 1 posts) starting at one end there are n section of a fence post and fence (each 5.5 feet long) and ends with a single 0.5 ft fence post so has length 5.5n+ .5.

In order that this be an integer number of feet, n must be odd so we can eliminate 28 and 50.

Is there a value of n that makes 5.5n+ .5= 17? That gives 5.5n= 16.5 and 16.5/5.5= 3.

Is there a value of n that makes 5.5n+ .5= 35? That gives 5.5n= 34.5 and 34.5/5.5= 6.272727....!

Is there a value of n that makes 5.5n+ .5= 39? That gives 5.5n= 38.5 and 38.5/5.5= 7.

 

Thank you.