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A board of length L feet is cut into two pieces such that th

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A board of length L feet is cut into two pieces such that th [#permalink] New post 20 Jun 2018, 09:42
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A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?

(A) \(\frac{L + 2}{2}\)

(B) \(\frac{2L +1}{2}\)

(C) \(\frac{L-1}{3}\)

(D) \(\frac{2L+ 3}{3}\)

(E) \(\frac{2L+1}{3}\)
[Reveal] Spoiler: OA

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Re: A board of length L feet is cut into two pieces such that th [#permalink] New post 23 Jun 2018, 06:40
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Carcass wrote:
A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?

(A) \(\frac{L + 2}{2}\)

(B) \(\frac{2L +1}{2}\)

(C) \(\frac{L-1}{3}\)

(D) \(\frac{2L+ 3}{3}\)

(E) \(\frac{2L+1}{3}\)


In this type I prefer to use number; however there are other ways to solve it -

Let
B = smaller side = 3

A = Larger side = 1 + (2*3) = 7

So the total length = 10.

Put the value of L in the option and we need 7 as an answer. Only option E yields the correct answer.

It is also advisable to start substituting the number L from option C as we will come to know whether we need to proceed towards option A or to option E.
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Re: A board of length L feet is cut into two pieces such that th [#permalink] New post 13 Dec 2018, 17:37
I was able to solve this using numbers, but it didn't work out using algebraic expressions. Can someone find out why? [quantity][/quantity]

Let's split up a line and translate the sentence given into an equation. Then the line can be broken up to a piece of length 2x+1 and a piece of length x. Then 3x+1 = L. Solving for L we get

x = (L-1)/3

Therefore, the length of the longer piece by substitution is 2x+1 = 2(l-1)/3

But this does not fit any of the answer choices. Please help. Thank you in advance.
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Re: A board of length L feet is cut into two pieces such that th [#permalink] New post 21 Jan 2019, 17:41
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Carcass wrote:
A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?

(A) \(\frac{L + 2}{2}\)

(B) \(\frac{2L +1}{2}\)

(C) \(\frac{L-1}{3}\)

(D) \(\frac{2L+ 3}{3}\)

(E) \(\frac{2L+1}{3}\)


We can let b= the length of piece B and (2b - 1) = the length of piece A and create the equation:

b + 2b - 1 = L

3b - 1 = L

3b = L + 1

b = (L + 1)/3

So the length of piece A is:

2(L + 1)/3 - 1

(2L + 2)/3 - 1

(2L + 2)/3 - 3/3 = (2L - 1)/3

Answer: E
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Re: A board of length L feet is cut into two pieces such that th   [#permalink] 21 Jan 2019, 17:41
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