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A nursery stocks only pine trees and maple trees. If the average heigh

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A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 13 Apr 2018, 03:23
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A nursery stocks only pine trees and maple trees. If the average height of a pine tree is 18 feet and the average height of a maple tree is 14 feet and 60% of the trees in the nursery are maple trees, what is the average height, in feet, for all trees at the nursery?

A. 15.2
B. 15.6
C. 16
D. 16.4
E. 16.8

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A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 13 Apr 2018, 04:50
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Bunuel wrote:
A nursery stocks only pine trees and maple trees. If the average height of a pine tree is 18 feet and the average height of a maple tree is 14 feet and 60% of the trees in the nursery are maple trees, what is the average height, in feet, for all trees at the nursery?

A. 15.2
B. 15.6
C. 16
D. 16.4
E. 16.8



Assume 60 maple trees and 40 pine trees

Average = (60*14 + 40*18)/100 = (840+720)/100 = (1560)/100 = 15.6

Hence option B = 15.6 is the answer.

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A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 13 Apr 2018, 13:29
Bunuel wrote:
A nursery stocks only pine trees and maple trees. If the average height of a pine tree is 18 feet and the average height of a maple tree is 14 feet and 60% of the trees in the nursery are maple trees, what is the average height, in feet, for all trees at the nursery?

A. 15.2
B. 15.6
C. 16
D. 16.4
E. 16.8

You can calculate the average height directly (because percents sum to 1). If 60% are maple, M, then 40% are pine, P

Average height =
(% of M)*(Height of M) + (% of P)*(Height of P)

Average height, \(A= (.6*14) + (.4*18)\)

\(A = 7.2 + 8.4\)

\(A = 15.6\)


ANSWER B
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Re: A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 16 Apr 2018, 17:09
Bunuel wrote:
A nursery stocks only pine trees and maple trees. If the average height of a pine tree is 18 feet and the average height of a maple tree is 14 feet and 60% of the trees in the nursery are maple trees, what is the average height, in feet, for all trees at the nursery?

A. 15.2
B. 15.6
C. 16
D. 16.4
E. 16.8



Since 60% of of the trees are maple, 40% must be pine; thus, the average height of all trees is:

0.4 x 18 + 0.6 x 14 = 7.2 + 8.4 = 15.6

Alternate Solution:

Let’s assume there are 10 trees in the nursery. This means that there are 6 maple trees and 4 pine trees. We can calculate a weighted average to determine the average height of all trees at the nursery:

(4 x 18 + 6 x 14)/10 = (72 + 84)/10 = 156/10 = 15.6 feet

Answer: B
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Re: A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 28 Apr 2018, 19:03
Take base as 10 so there are 6 maple trees and 4 pine trees

(6*14+4*18)/10 =15.6

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Re: A nursery stocks only pine trees and maple trees. If the average heigh  [#permalink]

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New post 28 Apr 2018, 19:11
Option B

(0.4 x 18) + (0.6 x 14) = 7.2 + 8.4 = 15.6
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Re: A nursery stocks only pine trees and maple trees. If the average heigh &nbs [#permalink] 28 Apr 2018, 19:11
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