Question 1058002: A circular plot of ground is to be enclosed with posts. If the posts are placed a ft. apart, the amount needed will be 150 short. If placed 1 yard apart, the amount will be 70 over. Determine circumference of plot.
Circumference of circle = pi * diameter.
Unsure how to proceed. Thanks.
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
A circular plot of ground is to be enclosed with posts. If the posts are placed a ft. apart, the amount needed will be 150 short.
If placed 1 yard apart, the amount will be 70 over. Determine circumference of plot.
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Let x be the circumference length, in feet.
The condition "If the posts are placed a ft. apart, the amount needed will be 150 short" means
x = n + 150, (1)
where "n" is the number of posts stocked at the site.
The condition "If placed 1 yard apart, the amount of posts will be 70 over." means
x/3 = n - 70. (2) ( 1 yard == 3 ft )
From (1), express n = x-150 and substitute it into (2) replacing n. You will get
x/3 = x - 150 - 70, or
2x/3 = 220.
Then x =  = 330.
Answer. The circumference is 330 ft.
The number of posts stocked at the site, is 330-150 = 180.
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