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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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Updated on: 23 Jul 2017, 23:40
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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

Attachment:

diagram.jpg [ 10.68 KiB | Viewed 5015 times ]

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Originally posted by carcass on 23 Jul 2017, 09:32.
Last edited by Bunuel on 23 Jul 2017, 23:40, edited 1 time in total.
Edited the question.
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Re: As shown in the diagram above, a lever resting on a fulcrum has weight  [#permalink]

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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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05 Sep 2017, 04:49
carcass wrote:

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

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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07 Sep 2017, 15:29
carcass wrote:

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

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

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

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18 Oct 2018, 07:05
carcass wrote:

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

Attachment:
diagram.jpg

The algebraic way is to write it as 50 * (d2 - 4) = 30d2

Or d1 = d2 - 4

We can pick from the answer choices a number that makes them equal.

If we pick d2 = 10

then 30*10 = 300
50 * 6 = 300

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

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05 Feb 2019, 07:27
Re: As shown in the diagram above, a lever resting on a fulcrum has weight   [#permalink] 05 Feb 2019, 07:27
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