Lesson: Applications on Systems of Inequalities Mathematics

In this lesson, we will learn how to solve applications of systems of inequalities by translating each condition into an inequality.

Lesson Plan

Objectives

Students will be able to

form a system of inequalities from a given real-world situation,
solve a real-world problem involving systems of inequalities.

Prerequisites

Students should already be familiar with

solving systems of linear inequalities.

Exclusions

Students will not cover

applications that include only one inequality.

Sample Question Videos

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02:59
01:42

Lesson Worksheet

Q1:

A shepherd wants to build a rectangular sheep barn. The length of the barn must be more than 88 m and its perimeter must be less than 253 m. Derive the system of inequalities that describes the situation, denoting the length of the barn by and its width by .

Q2:

A teacher gave his students 100 minutes to solve a test that has two sections: section A and section B. The students had to answer at least 4 questions from section A and at least 6 questions from section B and answer at least 11 questions in total. If a girl answered each question in section A in 3 minutes and each question in section B in 6 minutes, derive the system of inequalities that would help to know how many questions she tried to solve in each section. Use to represent the number of questions answered from section A and to represent the number from section B.

Q3:

Anthony and Daniel went on a tour driving to Luxor and Aswan and took turns driving; each day Anthony drove for at least 4 hours and NO more than 8 hours, while Daniel drove at least 2 hours and less than 7 hours. The total time they drove daily was NO more than 9 hours. State the system of inequalities that describes the situation, using to represent the number of hours that Anthony drove and to represent the number of hours that Daniel drove.