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In this lesson, we will learn how to solve word problems using systems of inequalities.

Q1:

Pedro and AndrΓ© went on a tour driving to Luxor and Aswan and took turns driving; each day Pedro drove for at least 4 hours and NO more than 8 hours, while AndrΓ© 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 Pedro drove and to represent the number of hours that AndrΓ© drove.

Q2:

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 π₯ and its width by π¦ .

Q3:

A teacher gave his students 100 minutes to solve a test. The students had to solve at least 4 questions from Section A, 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 π₯ to represent the number of questions answered from Section A and π¦ to represent the number from Section B.

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