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Two trees have a combined height of 60 feet, and the taller tree is x

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Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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New post 19 Aug 2018, 09:40
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86% (01:30) correct 14% (01:45) wrong based on 46 sessions

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Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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New post Updated on: 20 Aug 2018, 03:42
Let the height of the taller tree be a
Let the height of the shorter tree be b
Now, a+b = 60.
and also given that a = xb.
Substituting this in a+b, gives xb+b = 60 = b(1+x) = 60.
The height of the shorter tree, b = \(\frac{60}{1+x}\)
A is the answer.
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Originally posted by Chethan92 on 19 Aug 2018, 09:48.
Last edited by Chethan92 on 20 Aug 2018, 03:42, edited 1 time in total.
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Re: Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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New post 19 Aug 2018, 12:40
Bunuel 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) \(30 - 5x\)


Given
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)
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Re: Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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New post 20 Aug 2018, 09:43
let height of small tree is A and that of taller tree is B
so \(A+B=60\)
\(B=xA\)
so
\(A+xA=60\)
\(A(1+x)=60\)
\(A=\frac{60}{(1+x)}\)
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Re: Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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New post 22 Dec 2018, 11:38
Hi All,

We're told that two trees have a combined height of 60 feet and the taller tree is X times the height of the shorter tree. We're asked to find the height of the shorter tree in terms of X. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF the shorter tree is 10 feet tall and the taller tree is 50 feet tall, then X = 5. Thus, we're looking for an answer that equals 10 when we plug X=5 into it. After checking all five answers, there's only one that matches...

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Re: Two trees have a combined height of 60 feet, and the taller tree is x   [#permalink] 22 Dec 2018, 11:38
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