How much water should be added?

Question

A 10-gallon alcohol-water solution contains 30% pure alcohol. How much water should be added to produce the solution to 20% alcohol ?

Answer 1

Let A = gallons of alcohol

W = gallons of water

You start with 3 gallons of alcohol and 7 gallons of water (10 gallon mixture at 30%)

If you add x gallons of water, then the concentration is 3 gal A/(10 + x) gal Mix

Now, this must equal to 20%, therefore, {3/(10+x)}(100) = 20

So, 300/(10+x) = 20 or 300 = 200 + 20x or 20x = 100 or

x = 5 gallons So, add 5 gallons of W to get a 20% concentration.

Check: { 3/(10+5) }(100) = 300/15 = 20 √