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%?
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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 ,
4 0 % of 1 0 0 is 4 0
Let w = Amount of woman leaving
We're looking for 2 0 % of the new amount of people which will be 1 0 0 − w . However we also need the new amount of women which is 4 0 − w .
This means that
4 0 − w = 5 1 ⋅ ( 1 0 0 − w )
Re-arranging this gives us an equation for w
w = − 5 1 ⋅ ( 1 0 0 − w ) + 4 0
Expanding and simplifying it gives us
w = 5 w + 2 0
We're almost there, now we re-arrange it again to get
5 4 w = 2 0
Simplifying this gives us a value for w
w = 2 5
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
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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let x be the number of women to leave the room
1 0 0 − x 4 0 − x = 0 . 2 ⟹ 4 0 − x = 2 0 − 0 . 2 x ⟹ 2 0 = 0 . 8 x ⟹ x = 2 5