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The ratio of women to children at a certain party is 2 to 5

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NYC5648
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The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   01 Mar 2012, 14:08
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The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?

A. 30
B. 45
C. 60
D. 75
E. 90
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Bunuel
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   01 Mar 2012, 16:29
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NYC5648 wrote:
Hi everybody,

could please s.b. explain the steps to the following question:

The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?

Answer: 60

No answer choices.

Many thanks and a great weekend to all of you


Given: \(\frac{W}{C}=\frac{2}{5}\) and \(\frac{C}{M}=\frac{3}{4}\). Equate C's: \(\frac{W}{C}=\frac{2}{5}=\frac{6}{15}\) and \(\frac{C}{M}=\frac{3}{4}=\frac{15}{20}\) --> \(\frac{W}{\frac{C}{M}}=\frac{6}{\frac{15}{20}}\).

So, from \(\frac{W}{\frac{C}{M}}=\frac{6}{\frac{15}{20}}\) # of women, W, is a multiple of 6 and since it's given that \(13<w<20\) then \(w=18\) (the only multiple of 6 in this range). If \(W=18=3*6\) then \(M=3*20=60\).

Hope it's clear.
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   01 Mar 2012, 14:27
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When you have two different ratios, but one group appears in both ratios, you have to tranform both ratios in a way that lets you compare the ratios. You do this by finding the common denominator of both ratios, with the group that appears in both ratios in the denominator. So:

First write the ratio of men to childrean with childrean in the denominator->4:3

Now find a common denominator of both ratios, which is 15 in this case. Then you have the ratio of women to childrean as 6:15 and the ratio of men to childrean as 20:15

No combine all to get W:M:C as 6:20:15

If the number of women has to be between 13 and 20, 18 is the only option. So you multiply the combined ratio with 3 and get 60 men as your answer.
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   01 Mar 2012, 14:33
Many thanks for your rapid response. I understand your steps beside the last one:

"If the number of women has to be between 13 and 20, 18 is the only option. So you multiply the combined ratio with 3 and get 60 men as your answer."

Could you please explain to me why is has to be 18?

Thanks!
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   02 Mar 2012, 03:41
NYC5648 wrote:
Many thanks for your rapid response. I understand your steps beside the last one:

"If the number of women has to be between 13 and 20, 18 is the only option. So you multiply the combined ratio with 3 and get 60 men as your answer."

Could you please explain to me why is has to be 18?

Thanks!

As Bunuel wrote, it has to be a multiple of 6. For example if we would take 15 women(2.5 times as many as 6), the initial ratio would not provide integer values, because then we'd have a ratio of women to childrean of 5:12.5( initial ratio of 2:5 times 2.5) for example.
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   02 Mar 2012, 12:07
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Buneul,

if you may think this a shorter approach..


W:C = 2:5
C:M =3:4

When we combine ratios we get 6x:15x:20x

x has to be 3 for 6x >13 and <18
hence 20x=60
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   02 Mar 2012, 12:09
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shankar245 wrote:
Buneul,

if you may think this a shorter approach..


W:C = 2:5
C:M =3:4

When we combine ratios we get 6x:15x:20x

x has to be 3 for 6x >13 and <18
hence 20x=60


Yes, you can do this way too. Though it's basically the same.
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   03 Mar 2012, 12:40
Thank you to both of you!!!!
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   02 Sep 2014, 22:51
Woman : Children ................ Children : Men

2 ................ 5...............|| ....... 3 ............ 4

LCM of 3 & 5 = 15; Making it common

Woman : Children : Men

6 ............... 15 ....... 20

Woman are between 13 & 20

Only factor of 6 between 13 & 20 is 3; Multiplying by 3

Men = 20 * 3 = 60
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   06 Apr 2015, 22:22
Bunuel

I have a doubt. Please help me.

I did the problem like this:

w/c =2/5 c/m=3/5 therefore w:m=6:20

I further simplified the ratio of w:m as 3:10

now since the number of women is between 13 and 20.

Both 5 (5*3=15) and 6 (6*3=18) fit. Is it wrong to simplify the ratio like this?

thanks
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   07 Apr 2015, 05:15
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reubenoid wrote:
Bunuel

I have a doubt. Please help me.

I did the problem like this:

w/c =2/5 c/m=3/5 therefore w:m=6:20

I further simplified the ratio of w:m as 3:10

now since the number of women is between 13 and 20.

Both 5 (5*3=15) and 6 (6*3=18) fit. Is it wrong to simplify the ratio like this?

thanks


The number of women cannot be 15 because from W:C = 2:5 it follows that the number of women is a multiple of 2 (even).
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Re: The ratio of women to children at a certain party is 2 to 5 [#permalink] New post   23 Feb 2023, 15:03
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