In a student body the ratio of men to women was 1 to 4. After 140

Let the original constant of proportion be x.

After adding 140 men the new ratio of men to women becomes 2:3

This can be represented using:
\(\frac{(x+140)}{4x} = \frac{2}{3}\)
On solving for x,
\(3(x+140) = 8x\)
\(3x + 420 = 8x\)
\(5x = 420\)
we get \(x = 84\)

So the total original men and women are \(x + 4x = 5x\) or \(420\)

On adding the 140 men, the new total becomes -> \(420 + 140 = 560\)

Hence Option (B) is our choice.

Best,
Gladi


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(1x + 140)/4x = 2/3

8x = 3x + 420

5x = 420

5x = 42 * 2 * 5

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

Answer choice B

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Previously Male = x hence female = 5x
Total s-body after addition 5x+140
According to q stem ==> (x+140)/4x=2/3 ==> 3x+420 = 8x ==> 5x=420
Hence , Total s-body after addition 5x+140 = 560 Ans B

M : W = 1 : 4 = 3 : 12

New Ratio M: W = 2 : 3 = 8 : 12
total units = 8 + 12 = 20

Therefore, 5 units = 140
20 units = 140 * 5 = 560

Ans: B

Easy this one,

M = k and W = 4k

We have: (k+140)/4k =2/3

<=> 5k=420 => k = 84

So the number of men : M= 84 and the number of women: W= 4x84 = 336

Be careful the question asks us the total of men and women AFTER the additional men (140) were admitted !

The final answer is: Total = 84 + 336 + 140 = 560

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

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.

Answer: B
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(x + 140) /4x = 2/3
x = 84

5x = 420 (Men and women total)

420 + 140 = 560 (+additional men)
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The initial ratio of men to women was m:4m.

\(\frac{m+140}{4m} = \frac{2}{3}\)

\(3m+420 = 8m\)

\(5m = 420\)

\(m = 84\)

That's the initial number of men. We added 140, so we ended up with 224 men.
We have 4m = 336 women.

224+336 = 560

Answer choice B.

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