SOLUTION: a man is planning to fence the front part of his property with posts 2m apart. Short of money he decides to make the posts 3 m apart and uses 3 posts less. how wide is the property

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Question 545824: a man is planning to fence the front part of his property with posts 2m apart. Short of money he decides to make the posts 3 m apart and uses 3 posts less. how wide is the property?
Found 2 solutions by vleith, Edwin McCravy:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You will always need one more post then the number of sections in a fence. That is, for a single section you need 2 posts. For a two section fence, you will need 3 posts. Etc
So the length of the fence is the {{(NumberOfPosts -1) * (WidthOfSection)}}}
In this problem, the length of the fence does't cange. Only the number of posts and the width of the section. So
Let x be the number of posts in the 2m fence.
then
%28x-1%29+%2A+2+=+%28%28x-3%29-1%29+%2A+3
2x+-2+=+3x-12
x+=+10
If the number of posts in a 2m section fence is 10, then the length of the fence is %2810-1%29+%2A+2 = 18 m
Check your answer using the 3m values.
If x = 10, the 10-3 = 7 is the number of posts in a 3m section fence
%287-1%29+%2A+3+ = 18m

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
There is 1 more post than there are sections of fence between the posts.

He was originally planning to have N posts and N-1 2m sections of fence
between the posts, like this:

|  2m  |  2m  |  2m  |  2m  |  2m  |  ....  |  2m  |

But short of money he decided to have N-3 posts and N-4 3m sections of
fence between the posts instead, like this:

|   3m   |   3m   |   3m   |   3m   | ... |   3m   |


So  (N-1)×2 = (N-4)×3

    
     2(N-1) = 3(N-4)
     2N - 2 = 3N - 12
         -N = -10
          N = 10

So he was going to have 10 posts and 9 2m sections of fence between
them, so his property is 9×2m = 18m wide.

To check:  Instead he used 7 posts and 6 3m sections of fence between
them, so his property is 6×3m = 18m wide.  

So both ways his property is 18m wide.

Edwin