Solving Linear Inequalities in Real-Life Scenarios

A local bakery sells muffins and cookies. Each muffin costs $2 and each cookie costs $1. If the bakery wants to make at least $50 in sales, write a linear inequality to represent the situation and graph the feasible region.

• x + 2y ≤ 50

• 3x + y ≥ 50

• 2x + y < 50

• 2x + y ≥ 50

A school is planning a field trip and has a budget of $300. The cost per student is $15 for the trip. Write a linear inequality to represent the maximum number of students that can attend the trip and identify the feasible region on a graph.

• 15x ≤ 300, x ≤ 20

• 15x < 300, x < 20

• 20x ≤ 300, x ≤ 15

• 10x ≤ 300, x ≤ 30

A farmer has 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If the farmer has 120 hours of labor available, write a linear inequality to represent the situation and graph the feasible region.

• x + y ≤ 100, 2x + y ≤ 120

• x + y ≥ 100, 2x + y ≥ 120

• x + y = 100, 2x + y = 120

• x + y ≤ 80, 2x + y ≤ 100

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If the gym wants to earn at least $600 in membership fees, write a linear inequality and graph the feasible region for the number of basic and premium memberships sold.

• 30x + 50y = 600

• 30x + 50y ≥ 600

• 20x + 40y ≥ 600

• 30x + 50y ≤ 600

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor and each Type B gadget requires 2 hours. If the company has a maximum of 24 hours of labor available, write a linear inequality and identify the feasible region for the number of each type of gadget that can be produced.

• 3x + 2y ≤ 24

• 2x + 3y ≤ 24

• x + y ≤ 12

• 3x + 2y ≥ 24

A concert hall has a seating capacity of 500. If tickets for the front row cost $50 and tickets for the back row cost $20, and the concert hall wants to make at least $10,000, write a linear inequality to represent the situation and graph the feasible region.

• 50x + 20y ≥ 10000, x + y ≤ 500

• 50x + 20y = 10000, x + y = 500

• 50x + 20y ≤ 10000, x + y ≥ 500

• 50x + 20y ≥ 5000, x + y ≤ 300

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1,000 in sales, write a linear inequality to represent the situation and graph the feasible region for the number of shirts and pants sold.

• 25x + 40y = 1000

• 25x + 40y >= 1000

• 25x + 40y > 1000

• 25x + 40y <= 1000

A charity event is selling tickets for $15 each and donations are being accepted. If the goal is to raise at least $1,200, write a linear inequality to represent the situation and graph the feasible region for the number of tickets sold and donations received.

• 15x + y <= 1200

• x + y >= 1200

• 15x + y >= 1200

• 15x + y = 1200

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $10 and each non-vegetarian meal costs $15. If the restaurant wants to earn at least $800, write a linear inequality and graph the feasible region for the number of each type of meal sold.

• 10x + 15y ≤ 800

• 10x + 15y = 800

• 5x + 10y ≥ 800

• 10x + 15y ≥ 800

A tech company is developing two products: Product X and Product Y. Each Product X requires 4 hours of development and each Product Y requires 3 hours. If the company has a maximum of 30 hours available for development, write a linear inequality and identify the feasible region for the number of each product that can be developed.

• x + y ≤ 10

• 4x + 3y ≤ 30

• 2x + 5y ≤ 30

• 4x + 3y ≥ 30