Graphing Real-Life Constraints: Linear Inequalities Challenge

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 3 hours of labor. If he has a maximum of 240 hours of labor available, how many acres of each crop can he plant?

• 50 acres of corn and 50 acres of wheat

• 60 acres of corn and 40 acres of wheat

• 80 acres of corn and 20 acres of wheat

• 70 acres of corn and 30 acres of wheat

A school is organizing a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. If the number of students is represented by x, write the system of inequalities that represents the budget constraints and graph the solution.

• 0 <= x <= 14

• 0 <= x <= 20

• 0 <= x <= 5

• 0 <= x <= 10

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 4 hours of labor and each Type B gadget requires 2 hours. The company has a maximum of 40 hours of labor available. If the company wants to produce at least 5 Type A gadgets, what are the constraints on the number of gadgets produced?

• y <= 10

• x <= 5

• 4x + 2y <= 40, x >= 5, x >= 0, y >= 0

• 4x + 2y >= 40

A restaurant offers two types of meal packages: Package X and Package Y. Package X costs $10 and Package Y costs $15. The restaurant wants to sell at least 30 packages and make no more than $600 in total sales. Write the system of inequalities and interpret the solution graphically.

• x + y >= 40 and 10x + 15y <= 500

• x + y <= 25 and 10x + 15y <= 700

• x + y <= 30 and 10x + 15y >= 600

• The system of inequalities is: x + y >= 30 and 10x + 15y <= 600.

A local gym has a maximum capacity of 200 members. They offer two types of memberships: basic and premium. The basic membership costs $25 and the premium costs $40. If the gym wants to make at least $5000 in membership fees, what are the constraints on the number of each type of membership sold?

• x + y >= 200; 25x + 40y <= 5000

• x + y <= 150; 25x + 40y >= 6000

• x + y <= 200; 25x + 40y <= 4000

• x + y <= 200; 25x + 40y >= 5000

A charity event is selling tickets for a concert. Each ticket costs $30, and they want to sell at least 100 tickets to cover costs. If they can sell a maximum of 300 tickets, write the system of inequalities that represents the ticket sales and graph the solution.

• x >= 100, x <= 300

• x <= 100, x >= 300

• x >= 50, x <= 250

• x < 100, x > 300

A factory produces two products: Product A and Product B. Each Product A requires 3 hours of machine time and each Product B requires 2 hours. The factory has a total of 30 hours of machine time available. If they want to produce at least 5 of Product A, what are the constraints on the production of both products?

• x + y <= 15, x >= 5

• 3x + 2y <= 30, x >= 5

• 3x + 2y = 30, x >= 10

• 3x + 2y >= 30, x <= 5

A clothing store has a sale on shirts and pants. Shirts are $20 each and pants are $30 each. They want to sell at least 50 items and make no more than $1200 in total sales. Write the system of inequalities and interpret the solution graphically.

• x + y >= 50 and 20x + 30y = 1200

• x + y <= 50 and 20x + 30y <= 1200

• x + y <= 50 and 20x + 30y >= 1200

• The system of inequalities is: x + y >= 50 and 20x + 30y <= 1200.

A tech company is developing two software applications. Each application requires a different amount of resources: Application 1 requires 5 units and Application 2 requires 3 units. The company has a total of 40 units of resources available. If they want to develop at least 4 of Application 1, what are the constraints on the development of both applications?

• 5x + 3y <= 30, x >= 4, y >= 0

• 5x + 3y <= 40, x >= 4, x >= 0, y >= 0

• 5x + 3y <= 40, x >= 2, y >= 0

• 5x + 3y >= 40, x <= 4, x >= 0, y >= 0

A community center is planning a summer camp and has a budget of $2000. They plan to hire counselors at $200 each and provide activities at $50 each. If they want to hire at least 5 counselors, write the system of inequalities that represents the budget constraints and graph the solution.

• 150x + 75y ≤ 2000, x ≥ 5

• 200x + 50y ≤ 2000, x ≤ 5

• 200x + 50y ≤ 2000, x ≥ 5

• 200x + 50y ≤ 2500, x ≥ 3