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?

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.