Firefighter Practice Exam

How many ounces of water must be added to 24 ounces of a solution that is 44% alcohol to achieve a final concentration of 20% alcohol?

1. 33.1 ounces

2. 31 ounces

3. 28.8 ounces

4. 24 ounces

The correct answer is: 28.8 ounces

To determine how many ounces of water need to be added to dilute a solution from a higher concentration to a lower concentration, it is essential to understand the principle of dilution and how concentrations work. The initial solution contains 24 ounces of a liquid that is 44% alcohol. This means that the actual amount of alcohol in the solution is calculated as follows: Amount of alcohol = 24 ounces x 0.44 = 10.56 ounces of alcohol. Next, we want to dilute this solution so that the final concentration of alcohol is 20%. Let the amount of water that needs to be added be represented as \( x \) ounces. After adding water, the total volume of the new solution will be: Total volume = 24 ounces + \( x \) ounces. We want the alcohol to now comprise 20% of this new total solution. Therefore, we can set up the following equation for the desired concentration: 10.56 ounces of alcohol = 20% of (24 ounces + \( x \) ounces). This can be written mathematically as: 10.56 = 0.20(24 + \( x \)). Expanding this gives: 10.56 = 4.8 + 0.20