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How many liters of pure alcohol must be added to a 100-liter

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Director
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How many liters of pure alcohol must be added to a 100-liter [#permalink] New post 29 Dec 2005, 09:23
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19. How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

B) 20/3






Please show me how to solve, I've lost some piece of brain.
Manager
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 [#permalink] New post 29 Dec 2005, 09:35
20% of 100 litres = 20 litres alcohol
80 litres water
let x litres alcohol be added.

the ratio of alcohol to total solution = strength of the solution = 25%

(20+x)/(100+x)=0.25

solve this to get ur answer as 20/3
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Manager
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 [#permalink] New post 29 Dec 2005, 09:36
Let X be litres of pure alcohol that must be added. Since it is pure alcohol, the percent of alochol in it would be 100%

The sum of (Percentage of Alcohol * quantity for each of the parts) must satisfy the given condition

Therefore you can setup an equation

100 * X + 20 * 100 = 25 * (100 + X )

Solving for X, X = 20/3

Not sure if my explanation was any good ... let me know if you need to me to clarify any specifics
Director
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 [#permalink] New post 29 Dec 2005, 09:58
Thank you crazyfin and 5elements. Now it's clear.
Senior Manager
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 [#permalink] New post 29 Dec 2005, 12:21
20/3

the idea is to balance the volume and % of alcohol on both sides. (before dilution and after dilution)
CEO
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 [#permalink] New post 24 May 2007, 00:08
crazyfin wrote:
20% of 100 litres = 20 litres alcohol
80 litres water
let x litres alcohol be added.

the ratio of alcohol to total solution = strength of the solution = 25%

(20+x)/(100+x)=0.25

solve this to get ur answer as 20/3


heres the full answer.

(20+x)/(100+x)=0.25
(20+x) = 0.25(100+x)
20+x = 25 + .25x
20+1x = 25 + .25x
.75x = 5

x= 5/.75 = 20/3
  [#permalink] 24 May 2007, 00:08
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