Lesson: Applications on Systems of Inequalities Mathematics

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 .

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.

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.