Solve each problem. Alcohol MixtureBarak wishes to strengthen a mixture that is 10% alcohol to onethat is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?

Verified step by step guidance

1. Identify the initial amount of alcohol in the 10% mixture: Calculate 10% of 12 L.
2. Let x be the amount of pure alcohol to be added. The pure alcohol is 100% alcohol.
3. Set up the equation for the final mixture: The total alcohol in the new mixture will be the sum of the alcohol in the original mixture and the pure alcohol added, which should equal 30% of the total volume of the new mixture.
4. The equation will be: (0.10 * 12) + x = 0.30 * (12 + x).
5. Solve the equation for x to find the amount of pure alcohol to add.

Key Concepts

Concentration of Solutions

Concentration refers to the amount of solute (in this case, alcohol) present in a given volume of solution. It is often expressed as a percentage, indicating how much of the solution is made up of the solute. Understanding how to calculate and manipulate concentrations is essential for solving problems involving mixtures.

Mixture Problems

Mixture problems involve combining different quantities of substances to achieve a desired concentration or total amount. These problems typically require setting up equations based on the initial and final concentrations, as well as the volumes involved. Mastery of these problems is crucial for effectively solving real-world applications in chemistry and algebra.

Algebraic Equations

Algebraic equations are mathematical statements that express the equality of two expressions. In the context of mixture problems, setting up an equation allows you to represent the relationship between the amounts of different components. Solving these equations is key to finding unknown quantities, such as the amount of pure alcohol needed in this scenario.