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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 Updated on: 24 Sep 2012, 03:17
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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

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.

Originally posted by kalita on 24 Sep 2012, 03:12.
Last edited by Bunuel on 24 Sep 2012, 03:17, 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, 03:19
3
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, 13:05
1
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]

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New post 06 May 2018, 04:52
Top Contributor
kalita wrote:
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


One approach:

GIVEN: the ratio of boys to girls is 5 to 13
There are several possible cases that meet this condition:
- there are 5 boys and 13 girls
- there are 10 boys and 26 girls
- there are 15 boys and 39 girls
.
.
.
NOTE: We're also told that there are 72 more girls than boys.
So, as we continue listing possible cases, we'll keep track of the DIFFERENCE in the number of boys and girls
.
.
.
- there are 20 boys and 52 girls (there are 32 more girls than boys)
- there are 25 boys and 65 girls (there are 40 more girls than boys)
- there are 30 boys and 78 girls (there are 48 more girls than boys)
- there are 35 boys and 91 girls (there are 56 more girls than boys)
- there are 40 boys and 104 girls (there are 64 more girls than boys)
- there are 45 boys and 117 girls (there are 72 more girls than boys)

So, there must be 45 boys and 117 girls

Answer: C

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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 06 May 2018, 04:59
Top Contributor
kalita wrote:
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

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.


Another approach:
Let B = # of boys
Let G = # of girls

The ratio of boys to girls is 5 to 13.
We can write: B/G = 5/13
Cross multiply to get: 13B = 5G

There are 72 more girls than boys
We can write G = B + 72
Alternatively, we can write: G - 72 = B

We now have two equations:
13B = 5G
G - 72 = B

Take bottom equation and multiply both sides by 5 to get: 5G - 360 = 5B
Now replace 5G with 13B [since the top equation tells us that 13B = 5G]
We get: 13B - 360 = 5B
Add 36 to both sides: 13B = 5B + 360
Subtract 5B from both sides: 8B = 360
Solve: B = 45

Answer: C

Cheers,
Brent
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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 09 May 2018, 16:06
kalita wrote:
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


We can express the ratio B : G as 5 : 13, or 5x : 13x. We can create the equation:

13x - 72 = 5x

8x = 72

x = 9

So there are 5 x 9 = 45 boys.

Answer: C
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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 20 Jun 2018, 08:57
we know that ratio of girls to boys is 5:13, and there are 72 more girls than boys. So we can interpret that (13-5) 8x=72 or x=9, since we know that boys are 5x, they number must be 45 (C)
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Re: In a certain school, the ratio of boys to girls is 5 to 13. &nbs [#permalink] 20 Jun 2018, 08:57
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