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In a certain school, the ratio of boys to girls is 5 to 13.

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In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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New post 24 Sep 2012, 04:12
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In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117

[Reveal] Spoiler:
This is a pretty simple problem, however I was looking for purely algebraic way(s) to solve it. For some reason have trouble expressing it properly, please help to set it up.
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Sep 2012, 04:17, edited 1 time in total.
Edited the question.

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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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New post 24 Sep 2012, 04:19
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ikokurin wrote:
This is a pretty simple problem, however I was looking for purely algebraic way(s) to solve it. For some reason have trouble expressing it properly, please help to set it up.

In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?
A. 27
B. 36
C. 45
D. 72
E. 117


Given: \(\frac{b}{g}=\frac{5x}{13x}\), for some positive integer \(x\). So, the number of boys must be a multiple of 5. Only answer choice C fits.

Answer: C.

Alternately you can write: \(5x+72=13x\) --> \(x=9\) --> \(boys=5x=5*9=45\).

Answer: C.

Hope it helps.
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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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New post 24 Sep 2012, 14:05
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The ratio of b to G is 5:13 and the other data point is G are more than boys by 72...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 72. so 1 part corresponds to 72/8=9 and so
5 parts correspond to 5*9 = 45.


PS: always double check with the answer if u r using this approach.
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Re: In a certain school, the ratio of boys to girls is 5 to 13.   [#permalink] 24 Sep 2012, 14:05
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