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## In a student body the ratio of men to women was 1 to 4. After

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### In a student body the ratio of men to women was 1 to 4. After

by BTGModeratorVI » Mon Sep 14, 2020 8:49 am

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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

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### Re: In a student body the ratio of men to women was 1 to 4. After

by [email protected] » Thu Sep 17, 2020 6:06 am
BTGModeratorVI wrote:
Mon Sep 14, 2020 8:49 am
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
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

Cheers,
Brent

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### Re: In a student body the ratio of men to women was 1 to 4. After

by Neha sharma » Thu Sep 17, 2020 9:49 am
(1x + 140)/4x = 2/3

8x = 3x + 420

5x = 420

5x = 42 * 2 * 5

x = 84 * 5 + 140 = 420 + 140 = 560

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### Re: In a student body the ratio of men to women was 1 to 4. After

by gentvenus » Thu Sep 17, 2020 11:15 am
84 * 5 + 140
= 420 + 140
= 560

B

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### Re: In a student body the ratio of men to women was 1 to 4. After

by [email protected] » Mon Sep 21, 2020 6:22 am
BTGModeratorVI wrote:
Mon Sep 14, 2020 8:49 am
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
Solution:

We can re-express the ratio of 1 : 4 as 1x : 4x or x : 4x, where x = the number of men and 4x = the number of women. From this, we can create the equation:

(x + 140) / 4x = 2/3

Cross-multiplying, we obtain:

3(x + 140) = 2(4x)

3x + 420 = 8x

420 = 5x

84 = x

Therefore, after 140 new students were admitted, there were 84 + 4(84) + 140 = 560 students in the school.