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# The figure above shows part of a 42 1/2-foot fence in which 1/2-foot

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Math Expert
Joined: 02 Sep 2009
Posts: 43894
The figure above shows part of a 42 1/2-foot fence in which 1/2-foot [#permalink]

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01 Aug 2017, 08:34
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80% (02:37) correct 20% (02:23) wrong based on 11 sessions

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The figure above shows part of a 42 1/2-foot fence in which 1/2-foot wide vertical boards are arranged 3 feet apart. How many vertical boards are needed for the entire fence?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

[Reveal] Spoiler:
Attachment:

2017-08-01_2033.png [ 7.81 KiB | Viewed 327 times ]
[Reveal] Spoiler: OA

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The figure above shows part of a 42 1/2-foot fence in which 1/2-foot [#permalink]

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01 Aug 2017, 09:49

Every 1/2 foot wide vertical boards is arranged 3 feet apart and the total distance covered is 42 1/2 foot.

If x is the number of vertical boards, we would have (x-1) 3 feet distances.

So we can form the equation,
$$\frac{1}{2}*x + 3*(x-1) = 42\frac{1}{2}$$

$$\frac{x}{2} + (3x - 3) = 42\frac{1}{2}$$

$$\frac{x + 2(3x - 3)}{2} = \frac{85}{2}$$

$$\frac{x + 6x - 6}{2} = \frac{85}{2}$$

Multiplying by 2,
$$7x - 6 = 85$$
$$7x = 91$$
$$x = 13$$
Therefore, the number of vertical boards is 13(Option D)
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Re: The figure above shows part of a 42 1/2-foot fence in which 1/2-foot [#permalink]

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01 Aug 2017, 11:09
Since we are only looking for 1 value for this question, we can work backwards by using the answer choices to see what is the correct answer.

Let's start with picking (B) 11 as the number of 1/2 blocks required. 11*1/2 = 5.5'. Now these 11 blocks will be placed 3 feet apart therefore the distance between the 11 blocks is 10*3=30(since there will be 10 spaces between 11 blocks). Now we add 5.5 to 30 and get 35.5, but the total length is 42.5 there fore we need a bigger number, eliminate A and B.

Now let's try (D) 13. Using the same process, we get 13*1/2 = 6.5 and 12*3=36. 36+6.5 = 42.5, which is the total length we are looking for!

Re: The figure above shows part of a 42 1/2-foot fence in which 1/2-foot   [#permalink] 01 Aug 2017, 11:09
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