Problem Solving

Q.) A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts
along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would
surround this pasture if the width were doubled? (Assume that the space taken up by the fence posts is
negligible.)
A) 14
B) 16
C) 20
D) 22
E) 24

Someone explain.
Thanks,
Akshat

Q.) A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would surround this pasture if the width were doubled?

I'm getting 13 for this.

Length = 5*15 = 75

Width = 240 - (2*75) /2 = 45

Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts
along the length = 75/15 = 5 +1 = 6

Total = 7+6 = 13

Where did I go wrong?

OA is D

Length = 5*15 = 75 Width = 240 - (2*75) /2 = 45 Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts

along the length = 75/15 = 5 +1 = 6

U are correct till here....Now simply we have, 12 fences along the length which also includes the four corners.

Along the breadth, we have 7 or 14 on both sides, but this again includes the four corners. So, removing those 4 (since those are already counted for in Length), we are left with 10 along the breadth.

Adding the two ; 12+10 = 22. Option D.

Anurag

anuragvaid wrote:Length = 5*15 = 75 Width = 240 - (2*75) /2 = 45 Width doubled = 90

so along the width = 90/15= 6 +1 = 7 posts

along the length = 75/15 = 5 +1 = 6

U are correct till here....Now simply we have, 12 fences along the length which also includes the four corners.

Along the breadth, we have 7 or 14 on both sides, but this again includes the four corners. So, removing those 4 (since those are already counted for in Length), we are left with 10 along the breadth.

Adding the two ; 12+10 = 22. Option D.

Anurag

Where do these numbers come from?

Along the length there are 6 posts. Recognize that means a post at each end and 5 intervals of 15 feet to span the 6 posts.

So, the length is 5 x 15 or 75 feet. Given that the perimeter is 240 feet, the widths contribute 240 -(2x75) or 90 feet to the perimeter, meaning that the width is 45 feet.

Doubling the width therefore means the width ( now length) is 90 feet and the length (now width) is 75 feet.

Remembering from above that there is one more post than interval along a dimension there are 90/15 + 1 or 7 posts along the new length, or 14 in total for both lengths.

Likewise, along the 75 foot width, there are 75/15 +1 posts or 6.

HOWEVER, recognize that the two end posts of the width were already accounted for in the 14 determined above. So the number of INCREMENTAL posts along the width is 2 x (6-2) or 8.

Adding the posts along the length, 14, to the other posts along the width, 8, yields22

One of the keys here is that every corner post is counted TWICE, since it's effectively a vertex of the rectangle. The other key is that a side with 6 posts really has 5 fencelengths of 15, since we only need 1 fence to connect 2 posts, 2 lines to connect 3 posts, etc.