Question

prepare models using matrices to solve simple mixture problems

Answer 1

 

Mixture problems are excellent candidates for solving with systems of equations methods. These problems arise in many settings, such as when combining solutions in a chemistry lab or adding ingredients to a recipe. Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.

 

Learning to think of a mixture as a kind of rate is an important step in learning to solve these types of problems. Any situation in which two or more different variables are combined to determine a third is a type of rate.  Speed and time combine to give us distance. Wages and hours worked produce earnings.

 

In a similar way, lemon juice, sugar, and water mixed together make lemonade. The tartness of the drink will depend on the ratio of the quantities mixed together—that is a rate relationship. A lemonade mixture problem may ask how tartness changes when pure water is added or when different batches of lemonade are combined. 

 

The way to solve most mixture problems