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

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Math Expert
Joined: 02 Sep 2009
Posts: 55276
Two trees have a combined height of 60 feet, and the taller tree is x  [#permalink]

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19 Aug 2018, 09:40
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15% (low)

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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 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) $$30 - 5x$$

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

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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 = $$\frac{60}{1+x}$$
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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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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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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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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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