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There are 750 male and female participants in a meeting. Half the fema

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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 19 Aug 2018, 10:02
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There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

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Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 19 Aug 2018, 10:07
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225


m+f=750 -----1
f/2 + m/4 = democrats
750/3= democrats
2f+m=1000 ------2
subtracting 1 from 2
f=250
f who are democrats = f/2 = 125
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Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 07:03
sorry but i didn't get the explanation!
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Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 07:31
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Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225


There are 750 male and female participants in a meeting.
Let M = the number of males
Let F = the number of females
So, we can write: F + M = 750

One-third of all the participants are Democrats.
1/3 of 750 = 250
So, there are 250 Democrats in TOTAL

Half the female participants and one-quarter of the male participants are Democrats
(# of female Democrats) + (# of male Democrats) = TOTAL number of Democrats
So, we can write: (1/2)F + (1/4)M = 250
To eliminate the fractions, let's multiply both sides by 4 to get: 2F + M = 1000


How many of the Democrats are female?
We already know:
2F + M = 1000
F + M = 750
Subtract the bottom equation from the top equation to get: F = 250
So, there are 250 females, and we're told that 1/2 of them are Democrats
1/2 of 250 = 125

Answer: C

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Brent
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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 07:54
FAVEROL wrote:
sorry but i didn't get the explanation!



FAVEROL let me explain

let number of males be M
let number of females be F

\(\frac{1}{4}\)M = democrate males
\(\frac{1}{2}\)F = democrate females
Total number of democrates \(\frac{1}{3}*750 = 250\)

hence --- >

\(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\)

\(\frac{1}{2}\)F*\(250 = 125\)
So the Rest Part \(\frac{1}{4}= 125\) its number of male democrats


So number of female democrates is \(125\) :-)


Total number of females 250
Total number of males 500

Happy Studying :)

pushpitkc is my approach correct ? :-) thanks! :)
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Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 08:14
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225


Let total no of Female participants be 2f and total no of males be 4m and \(2f + 4m = 750\)

Now, \(f + m = 250\)

Plug in \(f = 250 - m\) in the first equation and check -

So, \(2( 250 - m) + 4m = 750\)

Or,\(500 - 2m + 4m = 750\)

Or,\(2m = 250\)

Or, \(m = 125\)

Now, \(f + m = 250\)

So, \(f + 125 = 250\)

Hence, f = 125 , Answer must be (C)
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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 10:57
1
dave13 wrote:
FAVEROL wrote:
sorry but i didn't get the explanation!



FAVEROL let me explain

let number of males be M
let number of females be F

\(\frac{1}{4}\)M = democrate males
\(\frac{1}{2}\)F = democrate females
Total number of democrates \(\frac{1}{3}*750 = 250\)

hence --- >

\(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\)

\(\frac{1}{2}\)F*\(250 = 125\)
So the Rest Part \(\frac{1}{4}= 125\) its number of male democrats


So number of female democrates is \(125\) :-)


Total number of females 250
Total number of males 500

Happy Studying :)

pushpitkc is my approach correct ? :-) thanks! :)



Hey dave13

Just one thing - how did you go from \(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\) -> \(\frac{1}{2}\)F*\(250 = 125\)

Your answer is absolutely correct - but this part if not so clear to me!

I'm thrilled that you are getting a lot of questions correct now but just want to be sure it is for the right reason :)
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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 12:09
pushpitkc wrote:
dave13 wrote:
FAVEROL wrote:
sorry but i didn't get the explanation!



FAVEROL let me explain

let number of males be M
let number of females be F

\(\frac{1}{4}\)M = democrate males
\(\frac{1}{2}\)F = democrate females
Total number of democrates \(\frac{1}{3}*750 = 250\)

hence --- >

\(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\)

\(\frac{1}{2}\)F*\(250 = 125\)
So the Rest Part \(\frac{1}{4}= 125\) its number of male democrats


So number of female democrates is \(125\) :-)


Total number of females 250
Total number of males 500

Happy Studying :)

pushpitkc is my approach correct ? :-) thanks! :)



Hey dave13

Just one thing - how did you go from \(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\) -> \(\frac{1}{2}\)F*\(250 = 125\)

Your answer is absolutely correct - but this part if not so clear to me!

I'm thrilled that you are getting a lot of questions correct now but just want to be sure it is for the right reason :)



Hey pushpitkc :-)

lemme explain my logic :-)

look at answer choices
(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

I know that \(\frac{1}{4}\)M +\(\frac{1}{2}\)F = \(250\)

So from 250 \(\frac{1}{2}\) will be female democrates and \(\frac{1}{4}\) will be male democrates

Say i will make this step \(\frac{1}{4}\) *250 = so i get 62 which doesnt work at all looking at answer choices

But if i multiply \(\frac{1}{2}\)* 250 i get 125 --- > that means \(\frac{1}{2}\)f equals 125 and the rest 250-125 =125 logically equals 1/4 of total male demacrates from total number of males

because if 125 is 1/4 i.e. 0.25 % the total number of males is 500

same logic if 125 equals 1/2 of number i.e. 0.50 the total number of females is 250

250+500 = 750

:-)
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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 13:09
FAVEROL wrote:
sorry but i didn't get the explanation!


Hello,

although you already have the explanation, the first three lines of my solution is nothing but the question stem ,rest just manipulation.
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There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 29 Aug 2018, 13:17
FAVEROL wrote:
sorry but i didn't get the explanation!


Here we have to take care of 2 distinctions.
1) participants
2) Democrats

To find :- #female Democrats=F/2,say F is #of female participants (Given half of the female participants are democrats )
Given :-
#participants=750=#male participants+#female participants or #male participants=750-#female participants–-----------(a)
#democrats=One-third of participants=750/3=250
Half of #female participants+one-fourth of male participants=#democrats=250----(b)
Since we need #female participants,so we have to substitute #male participants by a expression that relates to #female participants.(Expression (a) )

So expression(b) can be written as
#female participants/2+1/4*(750-#female participants)=250
Now the above expression is an algebra equation with 1 variable,so we can solve it.
F/2+750/4-F/4=250
F/2-F/4=250-750/4=250/4
Or. F/4=250/4
Multiply both sides by 2
F/2=125

Ans. (C)

Hope this helps.
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Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

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New post 03 Sep 2018, 18:58
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225


We can let f = the number of females and m = the number males in the meeting. So we have:

f + m = 750

Since 1/3 of the participants are Democrats, 750/3 = 250 are Democrats. So we have:

½f + ¼m = 250

Since m = 750 - f, we have:

½f + ¼(750 - f) = 250

Multiplying the equation by 4, we have:

2f + 750 - f = 1000

f = 250

Since half the female participants are Democrats, there are 125 female Democrats.

Answer: C
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Re: There are 750 male and female participants in a meeting. Half the fema &nbs [#permalink] 03 Sep 2018, 18:58
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