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. 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 to represent the number of questions answered from Section A and to represent the number from Section B.
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 to represent the amount of the first type and to represent the second type, state the system of inequalities that represents this situation.