SOLUTION: How much water must be added to a 2​-liter solution that contains 6​% extract of baneberry to get a solution that contains 4​% extract of​ baneberry?

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Question 1119116: How much water must be added to a 2​-liter solution that contains 6​% extract of baneberry to get a solution that contains 4​% extract of​ baneberry?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that 4% is 2%2F3 of 6%.
Add 1 liter of water.



Literal transcription with algebra to solve:
x, how much volume water to add;
2%2A0.06%2F%28x%2B2%29=0.04

2%2A6%2F%28x%2B2%29=4

3%2F%28x%2B2%29=1

3=x%2B2

highlight_green%281=x%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here are two other solution methods for this kind of problem....

(1) The 2 liters of 6% baneberry extract contain 2(.06) = 0.12 liters of extract.

After the water is added, those 0.12 liters of extract are now 4% of the mixture; that means the amount of the mixture is 0.12/0.04 = 3 liters.

So the amount of water added was 3-2 = 1 liter.

(2) You are mixing two ingredients with 6% and 0% extract. The percentage of the mixture, 4%, is "twice as close" to 6% as it is to 0%; that means the mixture must contain twice as much of the 6% ingredient as the 0% ingredient. So the 2 liters of the 6% ingredient is twice the amount of the 0% ingredient, making the amount of the 0% ingredient 1 liter.