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Two trees have a combined height of 60 feet, and the taller
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19 Aug 2018, 03:39
19 Aug 2018, 03:39
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Question Stats:
87% (00:56) correct
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Two trees have a combined height of 60 feet, and the taller tree is x times the height of the shorter tree. How tall is the shorter tree, in terms of x?
(A) \(\frac{60}{1+x}\)
(B) \(\frac{60}{x}\)
(C) \(\frac{30}{x}\)
(D) \(60 - 2x\)
(E) \(30 - 5x\)
(A) \(\frac{60}{1+x}\)
(B) \(\frac{60}{x}\)
(C) \(\frac{30}{x}\)
(D) \(60 - 2x\)
(E) \(30 - 5x\)
Re: Two trees have a combined height of 60 feet, and the taller
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10 Apr 2020, 14:03
10 Apr 2020, 14:03
1
Expert Reply
1) \(h_{t}+h_{s}=60\)
2) \(h_{t}=x*h_{s}\)
So, \(x*h_{s}+h_{s}=60\)
Or, \(h_{s}(x+1)=60\)
Or, \(h_{s}=\frac{60}{1+x}\)
Ans. (A)
2) \(h_{t}=x*h_{s}\)
So, \(x*h_{s}+h_{s}=60\)
Or, \(h_{s}(x+1)=60\)
Or, \(h_{s}=\frac{60}{1+x}\)
Ans. (A)
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Re: Two trees have a combined height of 60 feet, and the taller
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15 May 2020, 10:39
15 May 2020, 10:39
3
sandy wrote:
Two trees have a combined height of 60 feet, and the taller tree is x times the height of the shorter tree. How tall is the shorter tree, in terms of x?
(A) \(\frac{60}{1+x}\)
(B) \(\frac{60}{x}\)
(C) \(\frac{30}{x}\)
(D) \(60 - 2x\)
(E) \(30 - 5x\)
(A) \(\frac{60}{1+x}\)
(B) \(\frac{60}{x}\)
(C) \(\frac{30}{x}\)
(D) \(60 - 2x\)
(E) \(30 - 5x\)
Two trees have a combined height of 60 feet
Let S = the height of the shorter tree.
So, 60 - S = the height of the taller tree (since the two heights must add to 60)
The taller tree is x times the height of the shorter tree
In other words: (height of taller tree) = (x)(height of taller tree)
Substitute to get: 60 - S = (x)(S)
How tall is the shorter tree, in terms of x?
To answer the question, we must solve the following equation for S: 60 - S = (x)(S)
Add S to both sides to get: 60 = Sx + S
Factor out the S to get: 60 = S(x + 1)
Divide both sides by (x + 1) to get: 60/(x + 1) = S
Answer: A
Cheers,
Brent
