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In a forest, the ratio of pine trees to maple trees is 3:4, and the ratio of sycamore trees to maple trees is 4:5. If there are ten more sycamore trees than pine trees in the forest, how many pine trees are in the forest?
A. 150
B. 180
C. 190
D. 210
E. 240
A. 150
B. 180
C. 190
D. 210
E. 240
funnypanks
P:M=3:4..
S:M=4:5..
Get both ratios for M in same value..
So multiply P:M by 5 and S:M by 4..
P:M = 15:20....
S:M = 16:20..
Thus P:S = 15:16...
Now there are 10 more S than P...
So 16-15 or each UNIT is 10..
P is 15 UNITS, so 15*10=150
A
_________________
Suppose,
pine = 15x
Mapple = 20x
sycamore = 16x
therefore, sycamore - pine = 16x - 15x = x = 10;
SO pine tree = 15x = 150. Answer A.
Cheers.
_________________
pine = 15x
Mapple = 20x
sycamore = 16x
therefore, sycamore - pine = 16x - 15x = x = 10;
SO pine tree = 15x = 150. Answer A.
Cheers.
_________________
ScottTargetTestPrep
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funnypanks
We are given that the ratio of pine trees to maples trees is 3:4; thus:
pine : maple = 3x : 4x
We are also given that the ratio of sycamore trees to maples trees is 4:5; thus:
sycamore : maple = 4y : 5y
Since we see that maple = 4x in the first ratio and maple = 5y in the second ratio, we can multiply the first ratio by 5 and the second by 4 to create a three-part ratio.
pine : maple = 5(3x : 4x) = 15x : 20x
sycamore : maple = 4(4y : 5y) = 16y : 20y
Since the number of maple trees is the same in either ratio, we have 20x = 20y or x = y. Therefore, we can rewrite the ratio of sycamore to maple as:
sycamore : maple = 16x : 20x
Thus, we can write:
pine : maple : sycamore = 15x : 20x : 16x
Finally, since there are 10 more sycamore trees than there are pine trees, we can create the following equation to determine x:
16x = 10 + 15x
x = 10
Since x = 10, there are 15 x 10 = 150 pine trees.
Answer: A
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Abhishek009
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funnypanks
p : m = 3x : 4x
s : m = 4x : 5x ( or, m : s = 5x : 4x )
p : m : s = 15x : 20x : 16x
Now, 16x - 15x = 10
So, x = 10
Hence, total number of pine trees is 15*10 = 150 Pine trees...
Thus, answer will be (A) 150 !!
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Bunuel
Learn to combine the ratios for this questions
Answer: option A
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Bunuel
P/M = 3/4--------------(a)
S/M =4/5 or M/S = 5/4-----(b)
multiply (a) & (b) to get
P/S= 15/16
or S = 16P/15-------(c)
Also given P+10=S
substituting S from (c) we get
P+10= 16P/15
or P=150
Ans A
Abhishek009
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Bunuel
P : M = 3x : 4x => 15x : 20x
S : M = 4x : 5x +> 16x : 20x
So, P : M : S = 15x : 20x : 16x
Now, 16x - 15x = 10
Or, x = 10
So, No of Pine trees is 15*10 = 150
Thus, answer will be (A) 150
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ScottTargetTestPrep
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Bunuel
We are given that the ratio of pine trees to maple trees is 3:4 and that the ratio of sycamore trees to maple trees is 4:5. Thus:
pine trees : maple trees = 3 : 4
and
sycamore trees : maple trees = 4 : 5
Since we have maples trees in both ratios (4 and 5), let’s use the LCM of 4 and 5, which is 20, to equate the two ratios.
We can multiply the entire first ratio by 5 and the entire second ratio by 4, and we have:
pine trees : maple trees = 15 : 20
and
sycamore trees : maple trees = 16 : 20
Thus, our three-part ratio becomes:
pine trees : maple trees : sycamore tree = 15 : 20 : 16
or
pine trees : maples trees : sycamore tree = 15n : 20n : 16n (in which n is a multiplier)
Since there are ten more sycamore trees than pine trees, we have:
16n = 15n + 10
n = 10
Thus, there are 15 x 10 = 150 pine trees.
Answer: A
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