Applications of Systems of Linear Inequalities

Learning Outcomes

  • Write and graph a system that models the quantity that must be sold to achieve a given amount of sales

We can use what we now know about inequalities to write and graph a system of linear inequalities that models the amount of sales needed to obtain a specific amount of money.


Cathy is selling ice cream cones at a school fundraiser. She is selling two sizes: small (which has [latex]1[/latex] scoop) and large (which has [latex]2[/latex] scoops). She knows that she can get a maximum of [latex]70[/latex] scoops of ice cream out of her supply. She charges [latex]$3[/latex] for a small cone and [latex]$5[/latex] for a large cone.

Cathy wants to earn at least [latex]$120[/latex] to give back to the school. Write and graph a system of inequalities that models this situation.

Watch the video below for another example of solving an application using a system of linear inequalities.

We have seen that systems of linear equations and inequalities can help to define market behaviors that are very helpful to businesses. You’ll explore this idea more deeply later in this module.