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

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In a certain school, the ratio of boys to girls is 5 :13. If [#permalink] New post 08 Sep 2019, 02:30
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In a certain school, the ratio of boys to girls is 5 :13. If there are 72 more girls than boys, how many boys are there?

A. 27

B. 36

C. 45

D. 72

E. 117

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: In a certain school, the ratio of boys to girls is 5 :13. If [#permalink] New post 08 Sep 2019, 05:33
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Carcass wrote:
In a certain school, the ratio of boys to girls is 5 :13. If there are 72 more girls than boys, how many boys are there?

A. 27

B. 36

C. 45

D. 72

E. 117

Kudos for the right answer and explanation


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 :13. If [#permalink] New post 08 Sep 2019, 05:34
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Expert's post
Carcass wrote:
In a certain school, the ratio of boys to girls is 5 :13. If there are 72 more girls than boys, how many boys are there?

A. 27

B. 36

C. 45

D. 72

E. 117

Kudos for the right answer and explanation


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 :13. If   [#permalink] 08 Sep 2019, 05:34
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