Womens

Algebra Level 2

One room has 100 people. 40% of these people in this room are women. How many women need to leave the room for the percentage of women becomes 20%?


The answer is 25.

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5 solutions

let x x be the number of women to leave the room

40 x 100 x = 0.2 \dfrac{40-x}{100-x}=0.2 \implies 40 x = 20 0.2 x 40-x=20-0.2x \implies 20 = 0.8 x 20=0.8x \implies x = 25 \color{#D61F06}\boxed{x=25}

DarkMind S.
Nov 26, 2016

Since the original number of people is 100, 40% of women means that there are 40 women.

Now

Let the amount of women who left be X.

Then ( 40 - X ) / ( 100 - X ) = 20

40 - 20 = X - X/ 5

20 = ( 5X - X) / 5

100 = 4X / 5

X = 25 ,

Jack Rawlin
Dec 24, 2014

40 40 % of 100 100 is 40 40

Let w = w = Amount of woman leaving

We're looking for 20 20 % of the new amount of people which will be 100 w 100 - w . However we also need the new amount of women which is 40 w 40 - w .

This means that

40 w = 1 5 ( 100 w ) 40 - w = \frac {1}{5} \cdot (100 - w)

Re-arranging this gives us an equation for w w

w = 1 5 ( 100 w ) + 40 w = -\frac {1}{5} \cdot (100 - w) + 40

Expanding and simplifying it gives us

w = w 5 + 20 w = \frac {w}{5} + 20

We're almost there, now we re-arrange it again to get

4 w 5 = 20 \frac {4w}{5} = 20

Simplifying this gives us a value for w w

w = 25 w = 25

Let the number of women who leave the room be x.

The new number of women will be 40-x and the number of people in the room will be 100-x.

According to the question:

(40-x) = (20/100)(100-x)

5(40-x) = 200-5x = 100-x

100 = 4x

x = 25

Ruslan Abdulgani
Dec 8, 2014

Let the number of women who leave the room is x, so (40-x)/(100-x) = 1/5, the x=25.

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