Feasible Solutions in Linear Inequalities: A 9th Grade Quiz

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. Write an inequality to represent the maximum number of students that can attend. Analyze the solution region for the number of students.

• x ≤ 10

• x ≤ 14

• x ≤ 20

• x ≤ 12

A factory produces two types of toys, A and B. Each toy A requires 2 hours of labor and each toy B requires 3 hours. If the factory has 30 hours of labor available, write the inequality that represents the production limits. What are the feasible combinations of toys A and B?

• 4x + y ≤ 30

• 2x + 3y ≤ 30

• 2x + 3y ≥ 30

• x + 2y ≤ 30

A restaurant sells two types of sandwiches: vegetarian and meat. The profit from each vegetarian sandwich is $3 and from each meat sandwich is $5. If the restaurant wants to make at least $50 in profit, write the inequality and analyze the solution region for the number of sandwiches sold.

• 5x + 3y ≥ 50

• 3x + 5y ≥ 50

• 2x + 4y ≥ 50

• 3x + 2y ≥ 50

A gym has a maximum capacity of 200 members. If x represents the number of adult members and y represents the number of youth members, write an inequality to represent the membership limits. What are the feasible solutions for the number of adult and youth members?

• x + y ≥ 200; x + y must be less than 200

• x + y = 200; x, y must be positive integers

• x + y ≤ 200; feasible solutions are (x, y) such that x ≥ 0, y ≥ 0, and x + y ≤ 200.

• x + y < 200; x < 0, y < 0

A local charity is organizing a fundraiser and needs to sell at least 300 tickets. If each adult ticket costs $10 and each child ticket costs $5, write an inequality to represent the ticket sales. Analyze the solution region for the number of adult and child tickets sold.

• x + y ≥ 300

• x + y ≤ 300

• 10x + 5y = 300

• x + y < 300

A company produces two products, P1 and P2. Each product P1 requires 4 hours of machine time and each product P2 requires 2 hours. If the total machine time available is 40 hours, write the inequality that represents the production limits. What are the feasible combinations of products P1 and P2?

• 5x + 2y ≤ 40

• 4x + 3y ≤ 40

• 4x + 2y ≤ 40

• 3x + 2y ≤ 40

A bookstore has a shelf that can hold a maximum of 50 books. If x represents the number of fiction books and y represents the number of non-fiction books, write an inequality to represent the shelf space. What are the feasible solutions for the number of fiction and non-fiction books?

• x + y < 50, where x, y ≥ 0

• x + y = 50, where x, y > 0

• x + y ≤ 50, where x, y ≥ 0

• x + y ≥ 50, where x, y ≤ 0

A concert venue has a seating capacity of 800. If x represents the number of VIP tickets sold and y represents the number of general admission tickets sold, write an inequality to represent the seating limits. Analyze the solution region for the number of VIP and general admission tickets sold.

• x + y ≤ 800

• x + y < 800

• x + y = 800

• x + y ≥ 800

A clothing store has a sale on shirts and pants. Each shirt costs $15 and each pair of pants costs $25. If a customer has a budget of $200, write an inequality to represent the maximum number of shirts and pants that can be bought. What are the feasible combinations of shirts and pants?

• (0, 10)

• (5, 5)

• (4, 6)

• The feasible combinations of shirts and pants are: (0, 8), (1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1), (8, 0), (9, 5), (10, 3), (11, 1), (12, 0), (13, 0).