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If 2/3 of the number of women attending a certain dance is equal to 1/

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Bunuel
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If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   19 Jul 2018, 01:45
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If 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending, what fraction of those attending are women?

A. 2/5
B. 3/7
C. 5/7
D. 3/4
E. 5/6
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B
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   19 Jul 2018, 01:56
Bunuel wrote:
If 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending, what fraction of those attending are women?


Given,
2/3W = 1/2M
M=4/3W

Now,
Required fraction = W /(M + W)
= W / ((4/3)*W + W)
= W / (7 / 3W)
= 3/7

Hence, B.
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   19 Jul 2018, 01:57
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Bunuel wrote:
If 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending, what fraction of those attending are women?

A. 2/5
B. 3/7
C. 5/7
D. 3/4
E. 5/6


Instead of trying to calculate explicitly, we'll use easy numbers.
This is an Alternative approach.

Say there are 3 women. Then 2/3 of the women = 2 women are half the men meaning that there are 4 men.
So there are a total of 3 + 4 = 7 people
Then the fraction of women is 3/7.

(B) is our answer.
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   19 Jul 2018, 02:47
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Solution



Given:
• 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending

To find:
• What fraction of total people attending are women?

Approach and Working:

Let us denote women by “w” and men “m”.
• 2/3 w = ½ m
• w/m= 3/4
Thus, w/ (m+w)= 3/7

Hence, the correct answer is option B.

Answer: B
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   22 Jul 2018, 18:29
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Bunuel wrote:
If 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending, what fraction of those attending are women?

A. 2/5
B. 3/7
C. 5/7
D. 3/4
E. 5/6


Letting w = the total number of women and m = the total number of men, we can create the equation:

(2/3)w = (1/2)m

2w/3 = m/2

4w = 3m

4w/3 = m

The total number of people at the dance is (w + m). Thus, the percentage of women attending the dance is w/(w + m). We see that w/(w + m) = w/(w + 4w/3)

Multiplying by 3/3 we see that w/(w + 4w/3) becomes: :

3w/(3w + 4w) = 3w/7w = 3/7

Answer: B
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink] New post   11 Sep 2021, 07:27
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Bunuel wrote:
If 2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending, what fraction of those attending are women?

A. 2/5
B. 3/7
C. 5/7
D. 3/4
E. 5/6


Let w = # of women
Let m = # of men

2/3 of the number of women attending a certain dance is equal to 1/2 of the number of men attending
We can write: (2/3)w = (1/2)m
Rewrite as: 2w/3 = m/2
Cross multiply to get: 4w = 3m
Divide both sides of the equation by m to get: 4w/m = 3
Divide both sides of the equation by 4 to get: w/m = 3/4
This tells us that the ratio of women to men is 3 to 4.
In other words, for every 7 attendees, 3 are women and 4 are men.
In other words, 3/7 of the attendees are women.

Answer: B
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Re: If 2/3 of the number of women attending a certain dance is equal to 1/ [#permalink]
11 Sep 2021, 07:27
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