A solution is made by mixing 20% alcohol with 80% water. If 15 liters of alcohol are used, how many liters of the solution are there in total? - Redraw

Understanding the Context

A solution described as “20% alcohol” means that for every 100 liters of the mixture, 20 liters are alcohol and 80 liters are water. This ratio applies proportionally regardless of the total volume.

Let’s define:

• The volume of alcohol = 20% of the total solution
  
• The known quantity of alcohol = 15 liters

Let the total volume of the solution be x liters. Then,
20% of x = 15 liters
or
0.20 × x = 15

Solving for Total Volume

Key Insights

To find x, divide both sides by 0.20:
x = 15 ÷ 0.20
x = 75

Thus, the total volume of the solution is 75 liters.

Verifying the Water Content

To ensure accuracy, let’s verify:

• 20% of 75 liters = 0.20 × 75 = 15 liters alcohol ✔
  
• 80% of 75 liters = 0.80 × 75 = 60 liters water ✔

The values align perfectly with the stated composition.

Final Thoughts

Why This Calculation Matters

Understanding the total volume in concentration-based mixtures is essential in industries such as beverage production, pharmaceuticals, and chemical processing. Whether scaling up a recipe or maintaining consistent batch quality, accurate volume calculations ensure safety, compliance, and reliability.

Conclusion

If 15 liters of alcohol make up 20% of the total solution, the complete mixture contains 75 liters—15 liters of pure alcohol blended with 60 liters of water. This clear, formulaic approach enables quick and confident calculations every time.

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