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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3 men : 5 women
6 men : 10 women
9 men : 15 women = 24
So, correct answer is (B) 6.

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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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.

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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