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parkhydel
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A town parks director has specified that for every 3 aspen trees in th 05 Nov 2023, 08:55
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Reduced: Larch Increased: Fir
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45% (medium)

Question Stats:

71% (02:37) correct 29% (02:44) wrong based on 1814 sessions

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A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees, while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees. Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces. The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types.

Select for Reduced the type of tree that needs to be reduced in number, and for Increased the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information. Make only two selections, one in each column.
Reduced Increased
Aspen
Birch
Fir
Larch
Spruce
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Reduced: Larch Increased: Fir
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chetan2u
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A town parks director has specified that for every 3 aspen trees in th 03 Jan 2024, 01:49
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Quote:
A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees,
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=> Ratio A:B:F = 3:2:4
Quote:
while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees.
Show more
=> Ratio L:S:A = 1:3:2

Aspen trees are common in both ratios, so let us take them equal in two ratios by taking LCM of Aspen = LCM(3,2) = 6
=> Ratio A:B:F = 3:2:4 = 6:4:8
=> Ratio L:S:A = 1:3:2 = 3:9:6
Thus => Ratio L:S:A:B:F= 3:9:6:4:8


Quote:
Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces. The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types.
Show more
Presently L:S:A:B:F= 8:18:12:8:15
But we require them in ratio 3:9:6:4:8
A look at the ratio tells us that we have to multiply the required ratio by 2 to get close the actual ratio.

L:S:A:B:F= 2(3:9:6:4:8) = 6:18:12:8:16
Comparing with actuals 8:18:12:8:15, we see that three are same while number of L is more and number of F is less than the required.
So we will have to remove two of Larch and plant one fir.

Select for Reduced LARCH the type of tree that needs to be reduced in number, and for Increased FIR the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information.

sanyashah, hope it helps.
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A town parks director has specified that for every 3 aspen trees in th 05 Nov 2023, 10:55
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parkhydel


A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees, while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees. Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces. The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types.

Select for Reduced the type of tree that needs to be reduced in number, and for Increased the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information. Make only two selections, one in each column.
Show more
We can solve this question using below method:

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A town parks director has specified that for every 3 aspen trees in th 24 Jun 2024, 01:41
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                  A        B              F               L­            S
                  3        2              4                                     ------ ( multiply it by 2 )
                  2                                         1            3      -------(multiply by 3 )
--------------------------------------------------------------------------------------------------------------
                  6       4               8               3             9              => specified by the director
                  12     8               16             6             18            => mulitplied each by 2 

                   12    8               15             8              18               ==> current condition

Hence we can see that Fir    has to be increased to 16 from 15 and Larch   has to be decreased to 6 from 8.
 ­
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A town parks director has specified that for every 3 aspen trees in th 19 Jul 2025, 06:13
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parkhydel
A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees, while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees. Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces. The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types.

Select for Reduced the type of tree that needs to be reduced in number, and for Increased the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information. Make only two selections, one in each column.
Show more
Given Conditions

For every 3A we need 2B and 4F
For every 1L we need 3S and 2A

Given quantities as follows:
A = 12
B = 8
F = 15
L = 8
S = 18

We start analysing using L since A also depends on L and L is independent of everyone else.

For 8 L we would need 24S and 16A. However, we cannot increase both S and A since we are allowed to increase only one of the items.
Hence, we need to lower L.
We can see that if L is lowered to 6, then it matches with the S (18) and A (12) that we currently have. So let L be reduced to 6 for now.

Next, go to A. For 12A we need 12 *3/2 = 8 B which is already present. Next we need 12 * 4/3 = 16 F. However, we have 15 only so we increase F by 1.

So the answer would be reduce L and increase F.

This took me almost 3 minutes to solve on the first attempt. If anyone has a faster way to solve this please do share.
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A town parks director has specified that for every 3 aspen trees in th 21 Jul 2025, 20:36
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I'd take a look at the most helpful reply for this problem, their method seems fairly quick.
yazlal25
parkhydel
A town parks director has specified that for every 3 aspen trees in the downtown park, there should be exactly 2 birch trees and 4 fir trees, while for every 1 larch tree in the park, there should be exactly 3 spruce trees and 2 aspen trees. Currently, the park includes exactly 12 aspens, 8 birches, 15 firs, 8 larches, and 18 spruces. The parks director's specifications will be met by reducing the number of trees of exactly one of these types and increasing the number of trees of exactly one other of these types.

Select for Reduced the type of tree that needs to be reduced in number, and for Increased the type of tree that needs to be increased, to meet the parks director's specifications in the manner described in the given information. Make only two selections, one in each column.
Given Conditions

For every 3A we need 2B and 4F
For every 1L we need 3S and 2A

Given quantities as follows:
A = 12
B = 8
F = 15
L = 8
S = 18

We start analysing using L since A also depends on L and L is independent of everyone else.

For 8 L we would need 24S and 16A. However, we cannot increase both S and A since we are allowed to increase only one of the items.
Hence, we need to lower L.
We can see that if L is lowered to 6, then it matches with the S (18) and A (12) that we currently have. So let L be reduced to 6 for now.

Next, go to A. For 12A we need 12 *3/2 = 8 B which is already present. Next we need 12 * 4/3 = 16 F. However, we have 15 only so we increase F by 1.

So the answer would be reduce L and increase F.

This took me almost 3 minutes to solve on the first attempt. If anyone has a faster way to solve this please do share.
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A town parks director has specified that for every 3 aspen trees in th 08 Dec 2025, 03:34
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This question should not be tagged as Non-Math related
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A town parks director has specified that for every 3 aspen trees in th 08 Dec 2025, 03:41
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StanleyVu
This question should not be tagged as Non-Math related
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Edited the tag. Thank you!
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