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Worksheet: System of Linear Inequalities Word Problems

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 π‘₯ and its width by 𝑦 .

  • A π‘₯ β‰₯ 8 8 , 2 ( π‘₯ + 𝑦 ) < 2 5 3
  • B π‘₯ < 8 8 , 2 ( π‘₯ + 𝑦 ) < 2 5 3
  • C π‘₯ > 8 8 , π‘₯ + 𝑦 < 2 5 3
  • D π‘₯ > 8 8 , 2 ( π‘₯ + 𝑦 ) < 2 5 3
  • E π‘₯ > 8 8 , π‘₯ + 𝑦 > 2 5 3

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 π‘₯ to represent the number of questions answered from Section A and 𝑦 to represent the number from Section B.

  • A π‘₯ > 4 , 𝑦 > 6 , π‘₯ + 𝑦 β‰₯ 1 1 , 3 π‘₯ + 6 𝑦 ≀ 1 0 0
  • B π‘₯ β‰₯ 4 , 𝑦 β‰₯ 6 , π‘₯ + 𝑦 β‰₯ 1 1 , 3 π‘₯ + 6 𝑦 β‰₯ 1 0 0
  • C π‘₯ > 4 , 𝑦 β‰₯ 6 , π‘₯ + 𝑦 β‰₯ 1 1 , 3 π‘₯ + 6 𝑦 β‰₯ 1 0 0
  • D π‘₯ β‰₯ 4 , 𝑦 β‰₯ 6 , π‘₯ + 𝑦 β‰₯ 1 1 , 3 π‘₯ + 6 𝑦 ≀ 1 0 0
  • E π‘₯ ≀ 4 , 𝑦 ≀ 6 , π‘₯ + 𝑦 ≀ 1 1 , 3 π‘₯ + 6 𝑦 = 1 0 0

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 π‘₯ to represent the number of hours that Shady drove and 𝑦 to represent the number of hours that Fares drove.

  • A 4 ≀ π‘₯ ≀ 8 , 2 ≀ 𝑦 ≀ 7 , π‘₯ + 𝑦 ≀ 9
  • B 4 ≀ π‘₯ < 8 , 2 ≀ 𝑦 < 7 , π‘₯ + 𝑦 ≀ 9
  • C 4 ≀ π‘₯ ≀ 8 , 2 ≀ 𝑦 ≀ 7 , π‘₯ + 𝑦 < 9
  • D 4 ≀ π‘₯ ≀ 8 , 2 ≀ 𝑦 < 7 , π‘₯ + 𝑦 ≀ 9
  • E 4 ≀ π‘₯ ≀ 8 , 2 ≀ 𝑦 < 7 , π‘₯ + 𝑦 > 9

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 π‘₯ to represent the amount of the first type and 𝑦 to represent the second type, state the system of inequalities that represents this situation.

  • A π‘₯ > 5 , 𝑦 > 7 , 6 π‘₯ + 9 𝑦 < 5 5
  • B π‘₯ β‰₯ 5 , 𝑦 β‰₯ 7 , 6 π‘₯ + 9 𝑦 ≀ 5 5
  • C π‘₯ β‰₯ 6 , 𝑦 β‰₯ 9 , 5 π‘₯ + 7 𝑦 < 5 5
  • D π‘₯ β‰₯ 5 , 𝑦 β‰₯ 7 , 6 π‘₯ + 9 𝑦 < 5 5
  • E π‘₯ β‰₯ 6 , 𝑦 β‰₯ 9 , 5 π‘₯ + 7 𝑦 ≀ 5 5