Mastering Graphing & Solving Linear Inequalities

A farmer has 100 meters of fencing to create a rectangular pen for sheep. The length of the pen must be at least 20 meters. Write a system of inequalities to represent the possible dimensions of the pen and graph the solution.

• L + W ≥ 50, L ≤ 20

• L + W = 100, L ≥ 10

• L + W ≤ 60, L ≥ 25

• L + W ≤ 50, L ≥ 20

A school is planning a field trip and has a budget of $500. Each student ticket costs $15 and each adult ticket costs $20. Write a system of inequalities to represent the number of student and adult tickets they can purchase, and graph the solution.

• 15x + 25y ≤ 500, x ≥ 0, y ≥ 0

• 20x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 10x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 15x + 20y ≤ 500, x ≥ 0, y ≥ 0

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. The company has a maximum of 12 hours of labor available. Write a system of inequalities to represent the production limits and graph the solution.

• The system of inequalities is: 2x + 3y ≤ 12, x ≥ 0, y ≥ 0.

• 2x + y ≤ 12, x ≥ 0, y ≥ 0

• 2x + 3y ≥ 12, x ≥ 0, y ≥ 0

• x + y ≤ 12, x ≥ 0, y ≥ 0

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, while the premium membership costs $50. If the gym wants to earn at least $1,200 in a month, write a system of inequalities to represent the number of each type of membership sold and graph the solution.

• 20x + 40y >= 1200, x >= 0, y >= 0

• 30x + 50y <= 1200, x >= 0, y >= 0

• 30x + 50y >= 1000, x >= 0, y >= 0

• 30x + 50y >= 1200, x >= 0, y >= 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs and each vanilla cake requires 2 eggs. If the bakery has 30 eggs available, write a system of inequalities to represent the number of each type of cake that can be made and graph the solution.

• 3x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

A concert venue has a seating capacity of 500. Tickets for adults cost $25 and tickets for children cost $15. If the venue wants to earn at least $10,000 from ticket sales, write a system of inequalities to represent the number of adult and child tickets sold and graph the solution.

• x + y ≥ 500, 25x + 15y ≤ 10000

• x + y ≤ 300, 25x + 15y ≥ 15000

• x + y = 500, 25x + 15y = 10000

• x + y ≤ 500, 25x + 15y ≥ 10000

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. The store wants to make at least $1,000 in sales. Write a system of inequalities to represent the number of shirts and pants sold and graph the solution.

• The system of inequalities is: 20x + 30y >= 1000, x >= 0, y >= 0.

• 20x + 30y = 1000, x >= 0, y >= 0

• 20x + 30y <= 1000, x >= 0, y >= 0

• 10x + 15y >= 1000, x >= 0, y >= 0

A local restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $10 and each non-vegetarian meal costs $15. If the restaurant wants to earn at least $800 in a week, write a system of inequalities to represent the number of each type of meal sold and graph the solution.

• 10x + 15y <= 800, x >= 0, y >= 0

• 5x + 10y >= 800, x >= 0, y >= 0

• 10x + 20y >= 800, x >= 0, y >= 0

• 10x + 15y >= 800, x >= 0, y >= 0

A tech company is developing two products, X and Y. Each product X requires 4 hours of development and each product Y requires 2 hours. The company has a maximum of 20 hours available for development. Write a system of inequalities to represent the production limits and graph the solution.

• 2x + 3y ≤ 20, x ≥ 0, y ≥ 0

• 5x + y ≤ 20, x ≥ 0, y ≥ 0

• 3x + 4y ≤ 20, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 20, x ≥ 0, y ≥ 0