Writing and Solving Systems of Linear Inequalities

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

• L + W = 100, L ≥ 10

• L + W ≤ 60, L ≥ 25

• L + W ≤ 50, L ≥ 20

• 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 while staying within budget.

• 20x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 10x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 15x + 25y ≤ 500, x ≥ 0, y ≥ 0

• 15x + 20y ≤ 500, x ≥ 0, y ≥ 0

A bakery sells two types of cookies: chocolate chip and oatmeal. The bakery can make a maximum of 200 cookies in a day. They want to make at least 50 chocolate chip cookies. Write a system of inequalities to represent the number of each type of cookie they can bake.

• x + y = 200, y ≤ 50

• x + y ≤ 150, x ≥ 100

• x + y ≥ 200, x ≤ 50

• x + y ≤ 200, x ≥ 50

A gym offers two types of memberships: basic and premium. The gym can accommodate a maximum of 300 members. They want to have at least 50 premium members. Write a system of inequalities to represent the number of each type of membership they can sell.

• x + y <= 300, y >= 50

• x + y = 300, y = 50

• x + y >= 300, y <= 50

• x + y <= 250, y >= 100

A concert hall has a seating capacity of 800. Tickets for the front row cost $50, and tickets for the back row cost $30. The concert organizers want to sell at least 100 front row tickets. Write a system of inequalities to represent the ticket sales.

• x + y <= 800, x >= 100, x >= 0, y >= 0

• x <= 100

• y <= 0

• x + y >= 800

A company produces two products, A and B. Each product A requires 2 hours of labor, and each product B requires 3 hours. The company has a maximum of 60 hours of labor available per week. Write a system of inequalities to represent the production limits for products A and B.

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≥ 60, x ≥ 0, y ≥ 0

• x + y ≤ 20, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≥ 0

A local charity is organizing a food drive. They want to collect at least 300 cans of food. Each can of food costs $1 to transport. They have a budget of $200 for transportation. Write a system of inequalities to represent the number of cans they can collect and transport.

• x <= 300 and x <= 200

• x >= 300 and x >= 200

• x >= 200 and x <= 300

• x >= 300 and x <= 200

A clothing store has a sale on shirts and pants. They have a total of 150 items to sell, and they want to sell at least 30 shirts. Write a system of inequalities to represent the number of shirts and pants they can sell during the sale.

• x + y = 150, y ≥ 30

• x + y ≥ 150, x ≤ 30

• x + y ≤ 100, x ≥ 50

• x + y ≤ 150, x ≥ 30

A restaurant offers two types of meals: vegetarian and non-vegetarian. They want to serve at least 40 vegetarian meals and can serve a maximum of 100 meals in total. Write a system of inequalities to represent the meal options available.

• x + y >= 100, y <= 60

• x <= 40, x + y >= 100

• x >= 50, x + y <= 80

• x >= 40, x + y <= 100

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 team has a maximum of 40 hours available for development. Write a system of inequalities to represent the development time for products X and Y.

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 40, x ≥ 0, y ≥ 0