Graphing and Solving Systems of Inequalities: Real-World Scenarios

A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 3 hours of labor. If he has a total of 240 hours of labor available, write a system of inequalities to represent the situation and graph the solution.

• x + y >= 100, 2x + 3y >= 240, x <= 0, y <= 0

• x + y <= 100, 2x + 3y <= 240, x >= 0, y >= 0

• x + y <= 80, 2x + 3y <= 200, x >= 0, y >= 0

• x + y <= 120, 2x + 3y <= 300, x >= 0, y >= 0

A school is planning a field trip and has a budget of $500. The cost per student for the trip is $20, and the bus rental costs $200. Write a system of inequalities to represent the maximum number of students that can attend the trip and interpret the solution graphically.

• x <= 15

• x <= 20

• x <= 5

• x <= 10

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer can spend no more than $300 on memberships, write a system of inequalities to represent the situation and graph the solution.

• 30x + 50y ≥ 300, x ≤ 0, y ≤ 0

• The system of inequalities is: 30x + 50y ≤ 300, x ≥ 0, y ≥ 0.

• 30x + 50y = 300, x ≥ 0, y ≥ 0

• 30x + 50y ≤ 250, x ≥ 0, y ≥ 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake, and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write a system of inequalities to represent the maximum number of cakes that can be baked and interpret the solution graphically.

• 2x + 3y ≤ 10, x ≥ 0, y ≥ 0

• The system of inequalities is: 2x + y ≤ 10, x ≥ 0, y ≥ 0.

• x + 2y ≤ 10, x ≥ 0, y ≥ 0

• 2x + y ≥ 10, x ≥ 0, y ≥ 0

A concert hall has a seating capacity of 500. Tickets for the front row cost $50 each, and tickets for the back row cost $30 each. If the total revenue from ticket sales must be at least $15,000, write a system of inequalities to represent the situation and graph the solution.

• x + y ≥ 500, 50x + 30y ≤ 15000

• x + y = 500, 50x + 30y = 15000

• x + y ≤ 500, 50x + 30y ≥ 15000

• x + y ≤ 400, 50x + 30y ≥ 20000

A clothing store sells shirts and pants. Each shirt costs $15, and each pair of pants costs $25. If a customer has $200 to spend, write a system of inequalities to represent the maximum number of shirts and pants that can be purchased and interpret the solution graphically.

• The system of inequalities is: 15x + 25y <= 200, x >= 0, y >= 0.

• 15x + 20y <= 200, x >= 0, y >= 0

• 10x + 30y <= 200, x >= 0, y >= 0

• 20x + 25y <= 200, x >= 0, y >= 0

A charity event is selling tickets for $10 each and food for $5 each. If they want to raise at least $1,000 and can sell a maximum of 200 tickets and food items combined, write a system of inequalities to represent the situation and graph the solution.

• x + y >= 200

• x >= 10, y >= 5

• 10x + 5y >= 1000, x + y <= 200, x >= 0, y >= 0

• 10x + 5y <= 1000

A pet store has a limit of 50 animals. They sell cats and dogs, with each cat taking up 1 space and each dog taking up 2 spaces. If they want to have at least 10 cats, write a system of inequalities to represent the situation and interpret the solution graphically.

• x + 2y ≤ 40, x ≥ 5

• x + 2y ≤ 50, x ≥ 10

• x + y ≤ 50, x ≥ 10

• x + 2y ≤ 60, x ≥ 15

A local gym has a maximum capacity of 100 members. They offer two types of memberships: basic for $20 and premium for $40. If they want to earn at least $2,000 in membership fees, write a system of inequalities to represent the situation and graph the solution.

• x + y >= 100, 20x + 40y <= 2000

• x + y <= 100, 20x + 40y >= 2000

• x + y <= 50, 20x + 40y >= 1000

• x + y <= 100, 20x + 40y <= 2000

A farmer is growing two types of vegetables: carrots and lettuce. Each carrot plant requires 3 square feet, and each lettuce plant requires 2 square feet. If the farmer has 120 square feet available and wants to plant at least 10 carrot plants, write a system of inequalities to represent the situation and interpret the solution graphically.

• 3x + 2y ≥ 120 and x ≤ 10

• x + y ≤ 60 and x ≥ 5

• The system of inequalities is: 3x + 2y ≤ 120 and x ≥ 10.

• 2x + 3y ≤ 120 and y ≥ 10