Inequalities in Action: Writing & Solving Real-World Scenarios

A farmer has 100 acres of land 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 the farmer has a total of 120 hours of labor available, write a system of inequalities to represent the situation.

• x + y ≤ 80, 2x + y ≤ 100

• x + 2y ≤ 100, x + y ≤ 120

• 2x + 2y ≤ 120, x + y ≤ 90

• x + y ≤ 100, 2x + y ≤ 120

A school is planning a field trip and can take a maximum of 50 students. Each bus can hold 10 students. Write an inequality to represent the number of buses needed for the trip.

• 5b >= 25

• 15b <= 50

• b < 5

• 10b >= 50

A bakery sells two types of cookies: chocolate chip and oatmeal. The bakery can produce a maximum of 200 cookies per day. If the bakery wants to make at least 50 chocolate chip cookies, write a system of inequalities to represent the production limits.

• x + y < 200, x > 50

• x + y = 200, y ≤ 150

• 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. If they want at least 100 premium members, write a system of inequalities to represent the membership limits.

• x + y < 300, y < 100

• x + y ≤ 300, y ≥ 100

• x + y ≤ 250, y ≥ 150

• x + y ≥ 300, y ≤ 100

A company produces two products, A and B. Each product A requires 3 hours of labor and each product B requires 2 hours. If the company has 60 hours of labor available, write a system of inequalities to represent the production constraints.

• 3x + 2y ≤ 50, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 60, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≥ 0

• 3x + 2y ≥ 60, x ≥ 0, y ≥ 0

A concert hall has a seating capacity of 500. If tickets for VIP seats cost $100 and regular seats cost $50, and the total revenue from ticket sales must be at least $30,000, write a system of inequalities to represent the ticket sales.

• x + y >= 500, 100x + 50y <= 30000

• x + y <= 500, 100x + 50y = 30000

• x + y <= 500, 100x + 50y >= 30000

• x + y <= 400, 100x + 50y >= 25000

A restaurant has a budget of $1,000 for food supplies. If they spend $5 per meal for vegetarian meals and $10 per meal for non-vegetarian meals, write a system of inequalities to represent the budget constraints.

• 5x + 10y ≥ 1000, x ≥ 0, y ≥ 0

• 5x + 10y ≤ 500, x ≥ 0, y ≥ 0

• 5x + 10y ≤ 1000, x ≥ 0, y ≥ 0

• 5x + 10y ≤ 1000, 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 $1,000 in sales, write a system of inequalities to represent the sales goals.

• 20x + 30y <= 1000, x >= 0, y >= 0

• 20x + 30y >= 1000, x >= 0, y >= 0

• 10x + 15y >= 1000, x >= 0, y >= 0

• 20x + 30y = 1000, x >= 0, y >= 0

A charity organization is collecting donations. They want to collect at least $500 from individual donations and at least $300 from corporate donations. Write a system of inequalities to represent their fundraising goals.

• x >= 300, y >= 500

• x + y >= 800

• x >= 500, y >= 300

• x <= 500, y <= 300

A tech company is developing two products, X and Y. Each product X requires 4 hours of development and each product Y requires 3 hours. If the company has 48 hours available for development, write a system of inequalities to represent the development time constraints.

• 2x + 5y ≤ 48, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 48, x ≥ 0, y ≥ 0

• 4x + 3y ≥ 48, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 48, x ≥ 0, y ≥ 0