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Saplings are to be planted 30 feet apart along one side of a

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Saplings are to be planted 30 feet apart along one side of a [#permalink] New post 13 May 2018, 10:30
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Saplings are to be planted 30 feet apart along one side of a straight line 455 feet long. If the first sapling is to be planted at one end of the lane, how many saplings are needed?

(A) 18

(B) 16

(C) \(15\frac{1}{6}\)

(D) 15

(E) 14
[Reveal] Spoiler: OA

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Re: Saplings are to be planted 30 feet apart along one side of a [#permalink] New post 14 May 2018, 07:45
Expert's post
Carcass wrote:
Saplings are to be planted 30 feet apart along one side of a straight line 455 feet long. If the first sapling is to be planted at one end of the lane, how many saplings are needed?

(A) 18

(B) 16

(C) \(15\frac{1}{6}\)

(D) 15

(E) 14


Let's create a table and look for a pattern.

# of trees | space needed
1 tree: 0 feet
2 trees: 30 feet [2 trees separated by the necessary 30 feet]
3 trees: 60 feet
4 trees: 90 feet
5 trees: 120 feet
.
.
.

Notice that the space needed = (30)(number of trees - 1)
For example, for 5 trees we get: 120 feet = (30)(5 - 1)
So, if x = the number of trees, then the space needed = (30)(x - 1)

We know that 450 is divisible by 30, so we want:
450 = (30)(x - 1)
Divide both sides by 30 to get: 15 = x - 1
Solve: x = 16

Answer: B

Cheers,
Brent
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Re: Saplings are to be planted 30 feet apart along one side of a   [#permalink] 14 May 2018, 07:45
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