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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