Inequalities in Action: Graphing & Writing Systems

A farmer has a total of 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 maximum 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 <= 100, 2x + y <= 150, x >= 0, y >= 0

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

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

A school is organizing 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 number of students that can attend the trip and graph it.

• x >= 0 and x <= 20

• x >= 0 and x <= 15

• x >= 10 and x <= 30

• x >= 0 and x <= 25

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 cakes that can be made and graph it.

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 3y ≤ 30, 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 per month. If the gym wants to earn at least $1,000 in a month, write a system of inequalities to represent the number of each type of membership sold and graph it.

• { 30x + 50y >= 500, x >= 0, y >= 0 }

• System of inequalities: { 30x + 50y >= 1000, x >= 0, y >= 0 }

• { 30x + 50y <= 1000, x >= 0, y >= 0 }

• { 30x + 50y = 1000, x >= 0, y >= 0 }

A company produces two products, A and B. Each product A requires 4 hours of labor and each product B requires 2 hours of labor. If the company has a maximum of 40 hours of labor available, write a system of inequalities to represent the production limits and graph it.

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 30, x ≥ 0, y ≥ 0

A concert venue has a seating capacity of 500. Tickets for the front row cost $100 each, and tickets for the back row cost $50 each. If the venue wants to make at least $30,000 from ticket sales, write a system of inequalities to represent the ticket sales and graph it.

• x + y = 500, 100x + 50y = 30000

• x + y ≥ 500, 100x + 50y ≤ 30000

• x + y ≤ 400, 100x + 50y ≥ 25000

• x + y ≤ 500, 100x + 50y ≥ 30000

A charity event is selling two types of tickets: VIP and regular. VIP tickets cost $75 each, and regular tickets cost $25 each. If the charity wants to raise at least $2,000, write a system of inequalities to represent the ticket sales and graph it.

• 100x + 20y ≥ 2000, x ≥ 0, y ≥ 0

• 75x + 25y ≤ 2000, x ≥ 0, y ≥ 0

• 50x + 10y ≥ 2000, x ≥ 0, y ≥ 0

• 75x + 25y ≥ 2000, x ≥ 0, y ≥ 0

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. If the store wants to make at least $1,500 in sales, write a system of inequalities to represent the sales and graph it.

• 20x + 30y ≤ 1500, x ≥ 0, y ≥ 0

• 10x + 15y ≥ 1500, x ≥ 0, y < 0

• 20x + 30y = 1500, x < 0, y < 0

• System of inequalities: 20x + 30y ≥ 1500, x ≥ 0, y ≥ 0.

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $15 and each non-vegetarian meal costs $25. If the restaurant wants to earn at least $1,200, write a system of inequalities to represent the meal sales and graph it.

• {15x + 30y >= 1200, x >= 0}

• The system of inequalities is: {15x + 25y >= 1200, x >= 0, y >= 0}

• {10x + 20y >= 1200, x >= 0, y >= 0}

• {15x + 25y <= 1200, x >= 0, y >= 0}

A tech company produces laptops and tablets. Each laptop requires 5 hours of assembly and each tablet requires 3 hours. If the company has a maximum of 60 hours available for assembly, write a system of inequalities to represent the production limits and graph it.

• 4x + 2y ≤ 60, x ≥ 0, y ≥ 0

• 5x + 3y ≤ 60, x ≥ 0, y ≥ 0

• 6x + 3y ≤ 60, x ≥ 0, y ≥ 0

• 5x + 4y ≤ 60, x ≥ 0, y ≥ 0