SOLUTION: How many liters of water must be added to 7 liters of a 20% acid solution to obtain a 10% acid solution?

Question 280702: How many liters of water must be added to 7 liters of a 20% acid solution to obtain a 10% acid solution?
Found 2 solutions by oberobic, richwmiller:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With solutions, you need to keep track of how much 'pure' stuff you have or need to have.
In this case, you don't know how much solution you will end up with. You just know that you have 7 liters of a 20% solution. 7 * .2 = 1.4 liter of pure acid.
You do know that you will be adding pure water, which is 0% acid.
And you want to cut the acid from 20% down to 10%.
.
Logically, the 10% acid solution will have 1.4 liter of pure acid = 7 liters of the 20%.
.
.1x = 1.4, where x = total volume
.
x = 14 liters
.
This suggests that if you take 7 liters of 20% acid and add 7 liters of 0% acid, you end up with 14 liters of 10% solution.
.
Logically, you have to cut the acid solution in half, so it makes sense you have to double the volume.
.
Done
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
we can look at the problem from the point of view of water or acid.
water
.8*7+x=(7+x)*.90
x=7 liters of pure water
acid
.2*7=.1*(7+x)
x=7 liters of water as expected

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