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As shown in the diagram above, a lever resting on a fulcrum has weight

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As shown in the diagram above, a lever resting on a fulcrum has weight [#permalink]

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New post 23 Jul 2017, 09:32
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As shown in the diagram above, a lever resting on a fulcrum has weights of w1 pounds and w2 pounds, located d1 feet and d2 feet from the fulcrum. The lever is balanced and \(w_1d_1=w_2d_2\). Suppose w1 is 50 pounds and w2 is 30 pounds. If d1 is 4 feet less than d2, what is d2, in feet?


A. 1.5

B. 2.5

C. 6

D. 10

E. 20


[Reveal] Spoiler:
Attachment:
diagram.jpg
diagram.jpg [ 10.68 KiB | Viewed 1092 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 Jul 2017, 23:40, edited 1 time in total.
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Re: As shown in the diagram above, a lever resting on a fulcrum has weight [#permalink]

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New post 23 Jul 2017, 15:48
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carcass wrote:
Attachment:
diagram.jpg
As shown in the diagram above, a lever resting on a fulcrum has weights of w1 pounds and w2 pounds, located d1 feet and d2 feet from the fulcrum. The lever is balanced and \(w1d1=w2d2\). Suppose w1 is 50 pounds and w2 is 30 pounds. If d1 is 4 feet less than d2, what is d2, in feet?

A. 1.5

B. 2.5

C. 6

D. 10

E. 20


It should be D.

Lets call \(d2 = x\), \(d1\) would be \(x - 4\)

\(w1*d1 = w2*d2\)
\(50*(x-4) = 30*x\)
\(50x - 200 = 30x\)
\(20x = 200\)
\(x = 10\)
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Re: As shown in the diagram above, a lever resting on a fulcrum has weight [#permalink]

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New post 05 Sep 2017, 04:49
carcass wrote:
Image
As shown in the diagram above, a lever resting on a fulcrum has weights of w1 pounds and w2 pounds, located d1 feet and d2 feet from the fulcrum. The lever is balanced and \(w_1d_1=w_2d_2\). Suppose w1 is 50 pounds and w2 is 30 pounds. If d1 is 4 feet less than d2, what is d2, in feet?


A. 1.5

B. 2.5

C. 6

D. 10

E. 20


[Reveal] Spoiler:
Attachment:
diagram.jpg


The tricky part of this question lies here: "If d1 is 4 feet less than d2, what is d2, in feet? "

When you translate english to math, "d1 is 4 feet less than d2" does NOT mean d1 - 4 = d2. Order is important regarding subtraction, and whenever you see "less than" in english, you reverse the order in math.

Therefore, "If d1 is 4 feet less than d2" is translated as: d2 - 4 = d1.

1. d2 - 4 = d1
2. 50 x (d2 - 4) = 30 x (d2)
3. 50d2 - 200 = 30d2
4. 20d2 = 200
5. d2 = 10

Therefore, the answer is (D) 10

But, just in case you want to double check your work:

10 - 4 = 6
50 x 6 = 300
30 x 10 = 300

So, after plugging in the value of d2 to get the value of d1, we see that the equation is sound.

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Re: As shown in the diagram above, a lever resting on a fulcrum has weight [#permalink]

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New post 07 Sep 2017, 15:29
carcass wrote:
Image
As shown in the diagram above, a lever resting on a fulcrum has weights of w1 pounds and w2 pounds, located d1 feet and d2 feet from the fulcrum. The lever is balanced and \(w_1d_1=w_2d_2\). Suppose w1 is 50 pounds and w2 is 30 pounds. If d1 is 4 feet less than d2, what is d2, in feet?


A. 1.5

B. 2.5

C. 6

D. 10

E. 20


[Reveal] Spoiler:
Attachment:
diagram.jpg


We are given that w(1) = 50, w(2) = 30, and d(1) = d(2) - 4. If we let d(2) = d, we have:

50 x (d - 4) = 30 x d

50d - 200 = 30d

20d = 200

d = 10

Answer: D
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Re: As shown in the diagram above, a lever resting on a fulcrum has weight   [#permalink] 07 Sep 2017, 15:29
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