Graphing and Interpreting Linear Inequalities in Real Life

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by x and the width by y, write a linear inequality to represent the maximum area of the pen. Graph the inequality.

• x + y = 50, x ≥ 0, y ≥ 0

• x + y ≤ 50, x ≥ 0, y ≥ 0

• 2x + 2y ≤ 100, x ≥ 0, y ≥ 0

• x + y < 100, x ≥ 0, y ≥ 0

A school is planning a field trip and has a budget of $500. If each student ticket costs $15 and each teacher ticket costs $20, write a linear inequality to represent the number of students (x) and teachers (y) that can attend. Interpret the graph of this inequality.

• 10x + 15y ≤ 500

• 20x + 15y ≤ 500

• 15x + 25y ≤ 500

• 15x + 20y ≤ 500

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and gadget B requires 3 hours. If the company has 30 hours of labor available, write a linear inequality to represent the production limits. Graph the inequality and interpret the feasible region.

• 2x + 3y ≥ 30

• x + 2y ≤ 30

• 2x + 3y ≤ 30

• 4x + y ≤ 30

A concert hall has a seating capacity of 300. If tickets for adults (x) cost $10 and tickets for children (y) cost $5, write a linear inequality to represent the total number of tickets sold. Graph the inequality and explain the significance of the shaded area.

• x + y ≤ 300

• x + y = 300

• x + y < 300

• x + y ≥ 300

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 24 eggs, write a linear inequality to represent the number of cakes that can be made. Graph the inequality and discuss the implications for production.

• 2x + 3y ≤ 24

• x + 4y ≤ 24

• 3x + 2y ≤ 24

• 4x + y ≤ 24

A gym has a maximum capacity of 50 members. If x represents the number of adult members and y represents the number of child members, write a linear inequality to represent the membership limits. Graph the inequality and interpret the results in terms of gym capacity.

• x + y ≤ 50

• x + y = 50

• x + y ≥ 50

• x + y < 50

A local charity is organizing a food drive. They can collect a maximum of 200 cans of food. If each can of soup (x) counts as 2 cans and each can of vegetables (y) counts as 1 can, write a linear inequality to represent the collection limits. Graph the inequality and analyze the feasible solutions.

• 2x + 3y ≤ 200

• 3x + 2y ≤ 200

• x + y ≤ 200

• 2x + y ≤ 200

A clothing store has a sale on shirts and pants. If each shirt (x) costs $20 and each pair of pants (y) costs $30, and the total budget is $600, write a linear inequality to represent the spending limits. Graph the inequality and interpret the results in terms of clothing purchases.

• 10x + 15y ≤ 600

• 25x + 35y < 600

• 20x + 30y ≤ 600

• 20x + 30y = 600

A car rental company has a fleet of 100 cars. If x represents the number of economy cars and y represents the number of luxury cars, write a linear inequality to represent the total number of cars available for rent. Graph the inequality and discuss the implications for rental availability.

• x + y ≥ 100

• x + y ≤ 100

• x + y = 100

• x + y < 100

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 team has 40 hours available, write a linear inequality to represent the development limits. Graph the inequality and interpret the feasible region.

• 2x + 4y ≤ 40

• 4x + 3y ≤ 40

• 3x + 2y ≤ 40

• 4x + 2y ≤ 40