# Worksheet: System of Linear Inequalities Word Problems

In this worksheet, we will practice solving word problems using systems of inequalities.

**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 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.

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**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 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 , ,

**Q5: **

During a trip to the zoo you decide to buy peanuts and berries. A pack of peanuts costs and a pack of berries costs . 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

**Q6: **

A toy rocketβs height in feet above the ground is given by as a function of minutes after takeoff. Which of the following is the natural domain for this flight?

- Aall real numbers
- B
- C
- D
- E