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 peopleWe can write:

M + W = 24The ratio of men to women in a class is 3:5 We can write: M/W = 3/5

Cross multiply to get:

3W = 5MWe now have the following system:

M + W = 243W = 5MREWRITE

M + W = 24 as

M = 24 - WTake

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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