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Some boys and girls are having a car wash to raise money for a class

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Bunuel
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Some boys and girls are having a car wash to raise money for a class [#permalink] New post   26 Mar 2019, 23:16
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Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40% of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then 30% of the group are girls. How many girls were initially in the group?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
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itsanujsingh
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Re: Some boys and girls are having a car wash to raise money for a class [#permalink] New post   26 Mar 2019, 23:50
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Let total number of children in group be x
Number of girls=0.4x
No. Of girls after 2 girls left
0.4x-2=0.3x
X=20
No. Of girls initially in the group=0.4x=8

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Re: Some boys and girls are having a car wash to raise money for a class [#permalink] New post   27 Mar 2019, 01:32
Bunuel wrote:
Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40% of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then 30% of the group are girls. How many girls were initially in the group?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12


b+g=x
so
0.4x=girls
0.4x-2=0.3x
solve x= 20
so 0.4*20 ; 8
ImO C
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Re: Some boys and girls are having a car wash to raise money for a class [#permalink] New post   28 Mar 2019, 10:17
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We know the Total is sum of boys and girls. However, since 40% are girls - we have a ratio given of boys to girls = 60 : 40 = 6 : 4
(for ease of calculation, I would not simplify the ratio to 3:2) --->
Number of boys = 6X
Number of girls = 4X

It is important to use X because while 6:4 is a ratio, 6X and 4X are absolute values that we do not know yet.

Two girls leave, so number of girls (new) = 4X - 2
Two boys added, so number of boys (new) = 6X + 2

The ratio between these two new values = (4X-2)/(6X+2) ---> which is given to be equal to 30/70.
Solve (4X-2)/(6X+2) = 3/7
and we get X = 2.
Thus, number of girls initially = 4X = 8
Ans: C
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Re: Some boys and girls are having a car wash to raise money for a class [#permalink] New post   31 Mar 2019, 11:50
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Bunuel wrote:
Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40% of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then 30% of the group are girls. How many girls were initially in the group?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12


We can let the original number of girls = 0.4n and the original number of boys = 0.6n.

Since two girls leave and two boys arrive, leaving 30% of the group as girls, we have:

(0.4n - 2)/(n - 2 + 2) = 3/10

(0.4n - 2)/n = 3/10

10(0.4n - 2) = 3n

4n - 20 = 3n

n = 20

Therefore, there were 0.4 x 20 = 8 girls originally.

Answer: C
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Re: Some boys and girls are having a car wash to raise money for a class [#permalink] New post   24 Feb 2023, 08:23
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