Solve each problem. See Example 3. How many gallons of a 5% acid solution must be mixed with 5 gal of a 10% solution to obtain a 7% solution?

Key Concepts

Concentration of Solutions

Concentration refers to the amount of solute present in a given volume of solution, often expressed as a percentage. In this problem, we deal with different concentrations of acid solutions, specifically 5%, 10%, and the desired 7%. Understanding how to calculate the concentration is crucial for determining how much of each solution to mix.

Mixture Problems

Mixture problems involve combining different quantities of substances to achieve a desired outcome. In this case, we need to find the volume of a 5% acid solution that, when mixed with a 10% solution, results in a 7% solution. Setting up equations based on the total volume and the total amount of acid is essential for solving these types of problems.

Algebraic Equations

Algebraic equations are mathematical statements that express the equality of two expressions. To solve the mixture problem, we will set up an equation that represents the total amount of acid from both solutions. Solving this equation will allow us to find the unknown quantity of the 5% solution needed to achieve the desired concentration.