Graphical Solutions for Linear Inequalities in Real Scenarios

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write a system of inequalities to represent the number of students that can attend the trip. Analyze the solution graphically.

• 0 ≤ x ≤ 5

• 0 ≤ x ≤ 20

• 0 ≤ x ≤ 14

• 0 ≤ x ≤ 10

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. If the company has 30 hours of labor available, write a system of inequalities to represent the production limits. Solve the inequalities graphically.

• 2x + 3y ≤ 20, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≤ 0, y ≥ 0

• x + y ≤ 30, x ≥ 0, y ≥ 0

• The system of inequalities is: 2x + 3y ≤ 30, x ≥ 0, y ≥ 0.

A local gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, while the premium membership costs $50. If the gym wants to earn at least $2000 in a month, write a linear inequality to represent the number of each type of membership sold. Analyze the solution graphically.

• 30x + 50y ≥ 2000

• 20x + 40y ≥ 2000

• 30x + 50y = 2000

• 30x + 50y ≤ 2000

A concert hall has a seating capacity of 500. If tickets for the front row cost $50 and tickets for the back row cost $30, write a linear inequality to represent the total revenue needed to cover costs of at least $15,000. Analyze the solution graphically.

• 50x + 30y ≥ 20000, x + y ≤ 400

• 50x + 30y ≥ 15000, x + y ≤ 500

• 50x + 30y ≤ 15000, x + y ≥ 500

• 50x + 30y = 15000, x + y = 500

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1,000 in sales, write a system of inequalities to represent the number of shirts and pants that need to be sold. Solve the inequalities graphically.

• 25x + 40y >= 500, x >= 0, y >= 0

• 25x + 40y = 1000, x >= 0, y >= 0

• The system of inequalities is: 25x + 40y >= 1000, x >= 0, y >= 0.

• 25x + 40y <= 1000, x >= 0, y >= 0

A charity event is selling tickets for $10 each and donations are expected to be at least $500. Write a linear inequality to represent the total amount raised from ticket sales and donations. Analyze the solution graphically.

• 10x + d <= 500

• 5x + d >= 500

• 10x + d = 500

• 10x + d >= 500

A restaurant has a special offer where a meal costs $15 and a drink costs $5. If the restaurant wants to earn at least $300 in one evening, write a system of inequalities to represent the number of meals and drinks sold. Solve the inequalities graphically.

• 15x + 5y <= 300, x >= 0, y >= 0

• 10x + 5y >= 300, x >= 0, y >= 0

• 15x + 10y >= 300, x >= 0, y >= 0

• The system of inequalities is: 15x + 5y >= 300, x >= 0, y >= 0.

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. If the company has 40 hours available, write a system of inequalities to represent the maximum number of products that can be developed. Analyze the solution graphically.

• 4x + 2y ≤ 30, x ≥ 0, y ≥ 0

• The system of inequalities is: 4x + 2y ≤ 40, x ≥ 0, y ≥ 0.

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 40, x ≥ 0, y ≥ 0