SOLUTION: How much water should be added to 30mL of 20% alcohol solution to reduce the concentration to 15%? Please show me how to get this answer.

Question 499889: How much water should be added to 30mL of 20% alcohol solution to reduce the concentration to 15%? Please show me how to get this answer.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The answer to mixture problems always hinges on how much 'pure' stuff you have and how much you need.
.
30 mL of 20% alcohol solution means you have
30 * .2 = 6 mL of alcohol in the 30 mL solution.
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You don't care how much solution you end up with, but you want it to be 15% alcohol.
You will accomplish this by adding water, which is 0% alcohol.
.
So, how much would you need to have for 6 mL to be 15% of the total?
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Let x be the total volume.
.
.15x = 6
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x = 40
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So, if you have 6 mL of alcohol in 40 mL of solution, the solution is 15% alcohol.
Check this arithmetic.
.15*40 = 6.
.
You have 30 mL now. It contains the 6 mL of alcohol in question.
Therefore, you need to add 10 mL of water to make the total volume = 40 mL.
.
Done.
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