BTGModeratorVI wrote: ↑Sat Feb 15, 2020 3:27 pm
In a student body the ratio of men to women was 1 to 4. After 140 additional men were admitted, the ratio of men to women became 2 to 3. How large was the student body after the additional men were admitted?
(A) 700
(B) 560
(C) 280
(D) 252
(E) 224
Source: Official Guide
Answer:
B
Let's solve the question using two variables...
Let M = the number of men
Let W = the number of women
In a student body the ratio of men to women was 1 to 4
We can write: M/W = 1/4
Cross multiply to get: 4M = 1W
In other words:
4M = W
After 140 additional men were admitted, the ratio of men to women became 2 to 3
After 140 men are added, M + 140 = the NEW number of men
It's no additional women are added, W = the number of women
So, we can write: (M + 140)/W = 2/3
Cross multiply: 3(M + 140) = 2W
Expand:
3M + 420 = 2W
How large was the student body after the additional men were admitted?
We now have:
4M = W
3M + 420 = 2W
In the bottom equation, replace
W with
4M to get: 3M + 420 = 2(4M)
Simplify: 3M + 420 =8M
This means: 420 = 5M
So, M = 84
Plug M = 84 into
4M = W to get: 4(84) = W
So, W = 336
We now know that there were ORIGINALLY 84 men and 336 women, for a total of 420 people ORIGINALLY
After we add 140 men, the number of people = 420 + 140 = 560
Answer: B
Cheers,
Brent
