Exploring Inequalities: Real-World Feasible Regions Quiz

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 total of 240 hours of labor available, write an inequality to represent the feasible region for planting corn (x) and wheat (y).

• x + y ≥ 100, 2x + 3y ≤ 240

• x + y ≤ 80, 2x + 3y ≤ 200

• x + y ≤ 100, 2x + 3y ≥ 240

• x + y ≤ 100, 2x + 3y ≤ 240

A school is organizing a field trip and has a budget of $500. Each student ticket costs $15, and each adult ticket costs $20. Write an inequality to represent the number of student tickets (x) and adult tickets (y) that can be purchased without exceeding the budget.

• 15x + 25y ≤ 500

• 15x + 20y ≤ 500

• 10x + 15y ≤ 500

• 20x + 15y ≤ 500

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer can spend no more than $300 on memberships, write an inequality to represent the number of basic (x) and premium (y) memberships they can buy.

• 30x + 50y ≤ 300

• 20x + 40y ≤ 300

• 30x + 50y = 300

• 30x + 50y < 300

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake, and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write an inequality to represent the number of chocolate (x) and vanilla (y) cakes that can be baked.

• x + 2y ≤ 10

• 3x + y ≤ 10

• 2x + 3y ≤ 10

• 2x + y ≤ 10

A concert hall has a seating capacity of 2000. If tickets for the front row cost $50 each and tickets for the back row cost $30 each, write an inequality to represent the number of front row (x) and back row (y) tickets that can be sold without exceeding the seating capacity.

• x + y < 2000

• x + y ≤ 2000

• x + y ≥ 2000

• x + y = 2000

A clothing store sells shirts for $20 and pants for $30. If the store wants to make at least $600 in sales, write an inequality to represent the number of shirts (x) and pants (y) that need to be sold.

• 25x + 35y ≥ 600

• 20x + 30y ≤ 600

• 10x + 20y ≥ 600

• 20x + 30y ≥ 600

A charity event is selling tickets for $25 each and VIP tickets for $50 each. If they want to raise at least $1000, write an inequality to represent the number of regular tickets (x) and VIP tickets (y) that can be sold.

• 25x + 50y <= 1000

• 25x + 50y = 1000

• 30x + 40y >= 1000

• 25x + 50y >= 1000

A pet shelter has a limit of 50 animals. They have dogs and cats. If each dog counts as 2 animals and each cat counts as 1 animal, write an inequality to represent the number of dogs (x) and cats (y) that can be housed.

• x + y ≤ 50

• 3x + 2y ≤ 50

• 2x + 3y ≤ 50

• 2x + y ≤ 50

A local restaurant has a seating capacity of 100. If they have tables for 4 people and tables for 2 people, write an inequality to represent the number of 4-person tables (x) and 2-person tables (y) that can be set up without exceeding the seating capacity.

• 3x + 2y ≤ 100

• 4x + 2y ≤ 100

• 4x + y ≤ 100

• 2x + 4y ≤ 100

A factory produces two types of toys: dolls and cars. Each doll requires 3 hours to produce, and each car requires 2 hours. If the factory has 60 hours available for production, write an inequality to represent the number of dolls (x) and cars (y) that can be produced.

• 3x + y ≤ 60

• 3x + 2y ≥ 60

• 3x + 2y ≤ 60

• 2x + 3y ≤ 60