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Lesson: Using Systems of Inequalities to Solve Problems

Worksheet: Using Systems of Inequalities to Solve Problems • 7 Questions

Q1:

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.

  • A, ,
  • B, ,
  • C, ,
  • D, ,
  • E, ,

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

  • A, , ,
  • B, , ,
  • C, , ,
  • D, , ,
  • E, , ,

Q3:

Anthony finds two plumbers online: the first charges $20 per hour of labor, while the second charges a fixed charge of $40 per job plus an hourly labor charge of $15. After how many hours will the second plumber be cheaper than the first?

  • A5 hours
  • B6 hours
  • C8 hours
  • D2 hours
  • E4 hours

Q4:

During a trip to the zoo you decide to buy peanuts and berries. A pack of peanuts costs 73 pounds and a pack of berries costs 52 pounds. Given that you want to spend not more than pounds, write an inequality describing how many packs of each you could buy.

  • A
  • B
  • C
  • D

Q5:

Dorothy finds two landscape gardeners online: the first charges a fixed fee of $20 per job plus $15 per hour for labor, while the second charges a fixed fee of $90 but only $5 per hour for labor. After how many hours will the second gardener be cheaper than the first?

  • A2 hours
  • B3 hours
  • C7 hours
  • D5 hours
  • E6 hours
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