Lesson: System of Linear Inequalities Word Problems

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

Sample Question Videos

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Worksheet: System of Linear Inequalities Word Problems • 4 Questions • 3 Videos

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 𝑥 and its width by 𝑦 .

Q2:

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 𝑥 to represent the number of questions answered from Section A and 𝑦 to represent the number from Section B.

Q3:

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

Q4:

A carpenter wants to buy two types of nails; the first type costs 6 pounds per kilogram, and the second type costs 9 pounds per kilogram. He needs at least 5 kg of the first type and at least 7 kg of the second. He can spend less than 55 pounds. Using 𝑥 to represent the amount of the first type and 𝑦 to represent the second type, state the system of inequalities that represents this situation.

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