Solving a Mixture Problem using 2 variables

In this lesson, we learn how to solve a mixture problem using algebra by writing a system of equations with two variables. We are given a problem where Mia wants to make a punch by mixing apple juice and cranberry juice. We are shown a picture of what is going on before two equations are made from it, one that talks about the amount of juice and the other that talks about the cost. We then simplify these equations and use the substitution method to find out that Mia will need 75 quarts of apple juice and 25 quarts of cranberry juice. We then check this answer and find that it is correct.

This video shows how to solve the following mixture problem using algebra by writing a system of equations with 2 variables. Problem: Mia wants to make a punch by mixing some apple juice costing $2.25 per quart with cranberry juice costing $3.25 per quart. How many quarts of each should she use if she wants to make 100 quarts costing $2.50 per quart?

• How do you solve mixture problems in Algebra?
• If you want to make a punch by mixing apple juice costing $2.25 per quart with cranberry juice costing $3.25 per quart, how many quarts of each should she use to make 100 quarts costing $2.50 per quart?
• How can a picture help you solve a mixture problem?
• How do you know what two equations to write for a mixture problem?
• How do you solve a system of two equations with two unknowns?
• How do you solve a system of equations using substitution?
• How can you check to make sure your solution is correct in a mixture problem when you use systems of equations to solve?