SOLUTION: how many liters of a 20% alcohol should be added to 6 liters of a 40% alcohol solution so that the mixture is a 35% alcohol solution?

Question 932100: how many liters of a 20% alcohol should be added to 6 liters of a 40% alcohol solution so that the mixture is a 35% alcohol solution?
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
x the amount of the 20% solution
.20x + .40(6L) = .35(6L + x)
.05(6L)/.15 = x = 2L, the amount of the 20% solution

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
ow many liters of a 20% alcohol should be added to 6 liters of a 40% alcohol solution so that the mixture is a 35% alcohol solution?

Make this chart: | liters | percent as | liters of | | of liquid | a decimal | pure alcohol | -------------------------|-----------|------------|--------------| weaker solution | | | | stronger solution | | | | -------------------------|-----------|------------|--------------| medium strength solution | | | | Let x be the answer, x = no. of liters of weaker solution. And fill in what is given: | liters | percent as | liters of | | of liquid | a decimal | pure alcohol | -------------------------|-----------|------------|--------------| weaker solution | x | 0.20 | | stronger solution | 6 | 0.40 | | -------------------------|-----------|------------|--------------| medium strength solution | | 0.35 | | Now we get the number of liters of liquid by adding x and 6, getting x+6, | liters | percent as | liters of | | of liquid | a decimal | pure alcohol | -------------------------|-----------|------------|--------------| weaker solution | x | 0.20 | | stronger solution | 6 | 0.40 | | -------------------------|-----------|------------|--------------| medium strength solution | x+6 | 0.35 | | Next we get the number of liters of pure alcohol in each by multiplying the number of liters of liquid by the percentage of each: | liters | percent as | liters of | | of liquid | a decimal | pure alcohol | -------------------------|-----------|------------|--------------| weaker solution | x | 0.20 | 0.20x | stronger solution | 6 | 0.40 | 0.40(6) | -------------------------|-----------|------------|--------------| medium strength solution | x+6 | 0.35 | 0.35(x+6) | The equation comes from: Solve that and get x=2 liters. Edwin

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