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

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sandy
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Two trees have a combined height of 60 feet, and the taller [#permalink] New post   19 Aug 2018, 03:39
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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) 601+x
(B) 60x
(C) 30x
(D) 60−2x
(E) 30−5x
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Re: Two trees have a combined height of 60 feet, and the taller [#permalink] New post   10 Apr 2020, 14:03
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1) ht+hs=60
2) ht=x∗hs

So, x∗hs+hs=60
Or, hs(x+1)=60
Or, hs=601+x

Ans. (A)
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Re: Two trees have a combined height of 60 feet, and the taller [#permalink] New post   15 May 2020, 10:39
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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) 601+x
(B) 60x
(C) 30x
(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

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Re: Two trees have a combined height of 60 feet, and the taller [#permalink] New post   17 Jun 2021, 09:56
height of the taller tree be a
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 = 60/1+x

A is the answer
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Re: Two trees have a combined height of 60 feet, and the taller [#permalink]
17 Jun 2021, 09:56
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