Blaze Through the Firefighter Challenge 2025 – Ignite Your Skills & Shine Bright!

To determine how much distilled water needs to be added to 5 liters of 100% alcohol to achieve a 75% alcohol solution, it's essential to first understand the relationship between the volume of alcohol and the desired concentration.

Initially, there are 5 liters of pure alcohol, which consists of 100% alcohol. When you want to dilute this to a solution that is 75% alcohol, the total volume of the solution must contain a certain amount of pure alcohol.

The goal is to maintain 75% of the total solution as alcohol. If we let \( x \) be the volume of distilled water added, the total volume of the solution becomes \( 5 + x \) liters. The effective volume of alcohol in this solution remains at 5 liters because we haven't changed the amount of alcohol, only diluted it.

To find the correct amount of water to add, set up the equation that represents the setup:

\[

\frac{\text{Volume of alcohol}}{\text{Total volume of solution}} = \text{Desired concentration}

\]

Substituting the known values:

\[

\frac{5}{5 + x} = 0.75

\]

Now, solve for \( x \):

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