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D
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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 30963 times ]
23 Jul 2017, 16:48
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It should be D.
Lets call \(d2 = x\), \(d1\) would be \(x - 4\)
\(w1*d1 = w2*d2\)
\(50*(x-4) = 30*x\)
\(50x - 200 = 30x\)
\(20x = 200\)
\(x = 10\)
General Discussion
05 Sep 2017, 05:49
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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.
