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If the ratio of men to women in a class is 3:5 and the class has 24 p

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Bunuel
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If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 08:24
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If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15
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B
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 09:43
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Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15


total =24
ratio of men:women = 3:5

total = 3+5 = 8

24/8 =3

men = 9
women=15

15-9 =6

(B) imo
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 09:49
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3 men : 5 women
6 men : 10 women
9 men : 15 women = 24
So, correct answer is (B) 6.
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 10:20
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Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15


Total people = 24

ratio of Men and women = 3:5

Men = [3/(3+5)]*24 = (3/8)*24 = 9
WoMen = [5/(3+5)]*24 = (3/8)*24 = 15

Needed ratio of men and women = 1:1 i.e. equal number of men and women are needed

hence men needed = 15-9 = 6

Answer: option B
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 14:57
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Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15


The first 2 solutions are similar to my approach. However, we can also solve this question algebraically.

Let M = # of men in the class
Let W = # of women in the class

The class has 24 people
We can write: M + W = 24

The ratio of men to women in a class is 3:5
We can write: M/W = 3/5
Cross multiply to get: 3W = 5M

We now have the following system:
M + W = 24
3W = 5M

REWRITE M + W = 24 as M = 24 - W
Take 3W = 5M and replace M with 24 - W
We get: 3W = 5(24 - W)
Expand: 3W = 120 - 5W
Add 5W to both sides: 8W = 120
W = 15
So, there are 15 women in the class.
Since there are 24 people altogether, then there must be 9 men.

Wow many additional men would have to enroll to make the ratio of men to women 1:1?
If 6 men were to enroll, there would be 15 women and 15 men

Answer: B

Cheers,
Brent
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If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   24 Feb 2018, 15:51
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Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15

Ratio of men to women: \(\frac{3x}{5x}\)
Total of ratio parts: 3x + 5x = 8x
Total number of persons: 24
\(8x = 24\)
\(x = 3\) = multiplier that yields the actual number of men and women from the original ratio
Men = \(3x = (3)(3) = 9\)
Women = \(5x = (5)(3) = 15\)

To get a 1:1 ratio, we need the same number of men and women. We need 15 men. There are 9. We need 6 more men.

Answer B
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   25 Feb 2018, 12:40
Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15


Total = 24 people
men to women ratio is 3: 5
so men=9
women=15

now we don't knw how many men have to be enrolled in order to make the ratio 1:1
one thing has to be noticed here that 1: 1 means both men and women will be equal in no.
so, we have 15 women.
men 5
we need ( 15-9) men to make men and women equal in no.
so, 6 men would have to enroll.

approach 2: assign variable:

let's assume the no. of men will X that must have to enroll to keep the ratio 1: 1

9+x/15=1:1
9+x=15
x=6.
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   26 Feb 2018, 22:28
Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15

solu IMO B 3x+5x=24
8x=24, x=3
now men are 3*3=9 and women are 5*3=15 now to make ratio equal and increase boys equation will be 9+x/15=1/1 so x=6 and B is the correct option
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   11 Mar 2019, 08:12
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Bunuel wrote:
If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15



We can first determine the number of men and women with the equation:

3x + 5x = 24

8x = 24

x = 3

So there are 9 men and 15 women.

Since we want the ratio of men to women to be 1:1, there must be an equal number of men and women. Therefore, 15 - 9 = 6 more men should enroll.

Answer: B
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Re: If the ratio of men to women in a class is 3:5 and the class has 24 p [#permalink] New post   10 Feb 2024, 11:33
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