A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

Verified step by step guidance

1. Let x be the milliliters of the 34% silver nitrate solution.
2. Let y be the milliliters of the 4% silver nitrate solution.
3. Set up the equation for the total volume: x + y = 100.
4. Set up the equation for the silver nitrate content: 0.34x + 0.04y = 0.07 * 100.
5. Solve the system of equations to find the values of x and y.

Key Concepts

Concentration

Concentration refers to the amount of a substance (solute) present in a given volume of solution. It is often expressed as a percentage, indicating how much of the solute is contained in 100 parts of the solution. Understanding concentration is crucial for mixing solutions to achieve a desired final concentration.

Systems of Equations

A system of equations is a set of two or more equations with the same variables. In this context, it can be used to represent the relationships between the volumes of the two solutions and their respective concentrations. Solving the system allows us to find the exact amounts needed to achieve the desired mixture.

Mixture Problems

Mixture problems involve combining different quantities of substances to achieve a specific concentration or total amount. These problems typically require setting up equations based on the concentrations and volumes of the individual components, and they often involve algebraic manipulation to find the solution.