Applications of Linear Equations in Three Variables

Learning Outcomes

  • Solve applications using systems of equations in three variables

Systems can be helpful for solving real-world problems. In this example, we will write three equations that model sales at an art fair to learn how many prints should be sold to break even for the cost of the booth rental.


Andrea sells photographs at art fairs. She prices the photos according to size: small photos cost [latex]$10[/latex], medium photos cost [latex]$15[/latex], and large photos cost [latex]$40[/latex]. She usually sells as many small photos as medium and large photos combined. She also sells twice as many medium photos as large. A booth at the art fair costs [latex]$300[/latex].

If her sales go as usual, how many of each size photo must she sell to pay for the booth?

In the following video example, we show how to define a system of three equations in three variables that represents a mixture needed by a chemist.

Our last example shows you how to write a system of three equations that represents ticket sales for a theater that has three different prices for tickets.