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Intern
Joined: 27 Feb 2012
Posts: 33
Location: United States
Concentration: Finance, Marketing
GPA: 3.02
WE: Other (Education)

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18 May 2012, 11:16
2
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:37) correct 19% (01:52) wrong based on 31 sessions

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In the process of building my foundation, and I am complete stuck on this question.

If a pre-school admits 15 additional boys to its current population, the percentage of girls will be 40%. If currently the number of boys equals the number of girls, how many total students are currently enrolled in the school?

A. 30
B. 40
C. 60
D. 90
E. 120

I've seen the explanation, which leads you to the equations (b + 15)/(g + b + 15) = 3/5, g=b.

I don't understand why you would use g + b + 15 if you are searching for the current enrollment and why you would have b + 15/ g + b + 15. Is there any easier way to approach this question?

If someone can break this down for me, I'd REALLY appreciate it. Thanks!

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Math Expert
Joined: 02 Sep 2009
Posts: 58402

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18 May 2012, 13:46
Vixen wrote:
In the process of building my foundation, and I am complete stuck on this question.

If a pre-school admits 15 additional boys to its current population, the percentage of girls will be 40%. If currently the number of boys equals the number of girls, how many total students are currently enrolled in the school?

A. 30
B. 40
C. 60
D. 90
E. 120

I've seen the explanation, which leads you to the equations (b + 15)/(g + b + 15) = 3/5, g=b.

I don't understand why you would use g + b + 15 if you are searching for the current enrollment and why you would have b + 15/ g + b + 15. Is there any easier way to approach this question?

If someone can break this down for me, I'd REALLY appreciate it. Thanks!

Say currently there are $$g$$ girls and $$b$$ boys.

After 15 boys are admitted the number of boys would become $$b+15$$ and the total number of students $$g+(b+15)$$. We are told that the number of girls compose 40% of that number, so $$0.4(g+b+15)=g$$.

Now, since we are also told that currently the number of boys equals the number of girls (g=b) then when substituting $$b$$ by $$g$$ we get: $$0.4(g+g+15)=g$$ --> $$g=30$$ --> total=g+b=2g=60.

Hope it's clear.
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16 Jan 2019, 05:59
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