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]

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]

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]

24 Sep 2012, 12:18

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we know 5/13 and this is also equal to x/x+72. ---> 5x + 360 = 13x ---> x = 45.

Albeit, the Bunuel's approach is even more straight

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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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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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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.

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