Mastering Graphing and Solving Systems of Inequalities

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 1 hour of labor. If he has a total of 120 hours of labor available, write a system of inequalities to represent the situation and graph it.

• x + y <= 100, 2x + y <= 120, x >= 0, y >= 0

• x + y <= 120, 2x + y <= 150, x >= 0, y >= 0

• x + y <= 80, 2x + y <= 100, x >= 0, y >= 0

• x + y >= 100, 2x + y >= 120, 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 graph it.

• x <= 20, x >= 5

• x <= 15, x >= 0

• x <= 10, x >= 0

• x <= 12, x >= 1

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym wants to make at least $1,000 in membership fees, write a system of inequalities to represent the situation and graph it.

• 30x + 50y ≤ 1000, x ≥ 0, y ≥ 0

• 30x + 50y = 1000, x ≥ 0, y ≥ 0

• 30x + 50y ≥ 1000, x ≥ 0, y ≥ 0

• 20x + 40y ≥ 1000, x ≥ 0, y ≥ 0

A concert hall has a seating capacity of 500. Tickets for the front row cost $50, and tickets for the back row cost $30. If the concert hall wants to make at least $15,000 from ticket sales, write a system of inequalities to represent the situation and solve it.

• x + y ≤ 400, 50x + 30y ≥ 20000

• x + y ≤ 500, 50x + 30y ≥ 15000

• x + y = 500, 50x + 30y = 15000

• x + y ≥ 500, 50x + 30y ≤ 15000

A pet store has a limit of 40 animals it can house. They have dogs and cats, with each dog taking up 2 spaces and each cat taking up 1 space. Write a system of inequalities to represent the maximum number of dogs and cats the store can have and graph it.

• 2x + y >= 40, x >= 0, y >= 0

• The system of inequalities is: 2x + y <= 40, x >= 0, y >= 0.

• x + y <= 40, x >= 0, y >= 0

• x + 2y <= 40, x >= 0, y >= 0

A clothing store sells shirts and pants. Each shirt costs $15, and each pair of pants costs $25. If the store wants to make at least $1,200 in sales, write a system of inequalities to represent the situation and solve it.

• 15x + 25y <= 1200, x >= 0, y >= 0

• 15x + 25y >= 1200, x >= 0, y >= 0

• 10x + 30y >= 1200, x >= 0, y >= 0

• 20x + 20y >= 1200, x >= 0, y >= 0

A local charity is organizing a fundraiser. They plan to sell tickets for a dinner event at $40 each and raffle tickets at $5 each. If they want to raise at least $2,000, write a system of inequalities to represent the number of dinner and raffle tickets they need to sell and graph it.

• 50x + 2y >= 2000, x >= 0, y >= 0

• 40x + 5y >= 2000, x >= 0, y >= 0

• 30x + 10y >= 2000, x >= 0, y >= 0

• 20x + 8y >= 2000, x >= 0, y >= 0

A restaurant has a limit of 100 customers. Each table can seat 4 people, and each booth can seat 6 people. Write a system of inequalities to represent the maximum number of tables and booths the restaurant can have and solve it.

• 4x + 6y <= 100, x >= 0, y >= 0

• 2x + 4y <= 100, x >= 0, y >= 0

• 5x + 7y <= 100, x >= 0, y >= 0

• 3x + 5y <= 100, x >= 0, y >= 0

A sports team has a budget of $1,500 for new equipment. Each basketball costs $50, and each soccer ball costs $30. Write a system of inequalities to represent the maximum number of basketballs and soccer balls the team can purchase and graph it.

• 50x + 30y ≤ 1500, x ≥ 0, y ≥ 0

• 60x + 40y ≤ 1500, x ≥ 0, y ≥ 0

• 50x + 30y ≤ 1000, x ≥ 0, y ≥ 0

• 40x + 20y ≤ 1500, x ≥ 0, y ≥ 0