Mastering Graphing Linear Inequalities in Real-Life Scenarios

A local gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write a linear inequality to represent the number of classes they can attend. Graph the inequality.

• x ≤ 14

• x ≤ 10

• x ≤ 20

• x ≤ 12

A farmer has a budget of $200 to buy seeds for two types of crops: corn and wheat. Corn seeds cost $2 per packet and wheat seeds cost $3 per packet. Write a linear inequality to represent the number of packets of corn (x) and wheat (y) the farmer can buy. Interpret the graph of this inequality.

• x + 2y ≤ 200

• 2x + 3y ≤ 200

• 4x + y ≤ 200

• 2x + 3y = 200

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 linear inequality to represent the maximum number of students (x) that can attend the trip. Graph the inequality and interpret the results.

• x <= 10

• x <= 12

• x <= 14

• x <= 20

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 a maximum of 30 hours of labor available, write a linear inequality to represent the production of gadgets A (x) and B (y). Graph the inequality and explain the feasible region.

• 2x + 3y = 30

• 2x + 3y ≤ 30

• x + y ≤ 10

• 4x + 2y ≤ 30

A restaurant sells two types of sandwiches: vegetarian and meat. The vegetarian sandwich costs $5 and the meat sandwich costs $7. If the restaurant wants to make at least $200 in a day, write a linear inequality to represent the number of vegetarian (x) and meat (y) sandwiches they need to sell. Graph the inequality and interpret the graph.

• 5x + 7y ≥ 200

• 5x + 7y = 200

• 3x + 4y ≥ 200

• 5x + 7y < 200

A charity event aims to raise at least $1,000. Tickets are sold for $15 each and donations are accepted. If the number of tickets sold is represented by x and the total donations by y, write a linear inequality to represent this situation. Graph the inequality and discuss the implications.

• 15x + y ≥ 1000

• 15x + y ≤ 1000

• 15x + y = 1000

• 10x + y ≥ 1000

A bookstore sells fiction and non-fiction books. Fiction books are priced at $10 and non-fiction at $15. If the store wants to earn at least $300 in sales, write a linear inequality to represent the number of fiction (x) and non-fiction (y) books sold. Graph the inequality and interpret the results.

• 10x + 15y >= 300

• 15x + 10y >= 300

• 10x + 20y <= 300

• 5x + 10y >= 300

A concert venue has a seating capacity of 500. If tickets for the front row cost $50 and general admission tickets cost $30, write a linear inequality to represent the number of front row (x) and general admission (y) tickets that can be sold without exceeding capacity. Graph the inequality and explain the feasible solutions.

• x + y ≤ 500

• 2x + y ≤ 500

• x + y < 500

• x + 2y ≤ 500

A tech company has a budget of $1,200 for hiring interns. Each intern in the software department costs $300 and each intern in the marketing department costs $200. Write a linear inequality to represent the number of software (x) and marketing (y) interns they can hire. Graph the inequality and interpret the feasible region.

• 300x + 200y ≥ 1200

• 300x + 200y = 1200

• 100x + 400y ≤ 1200

• 300x + 200y ≤ 1200