Real-Life Linear Inequalities: Write & Graph Scenarios

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost if a member wants to spend no more than $100 in a month. Graph the inequality.

• 30 + 5x < 100, x < 14

• 30 + 5x = 100, x = 14

• 30 + 5x ≤ 100, x ≤ 14

• 30 + 5x ≥ 100, x ≥ 14

A farmer has 200 acres of land and wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour. If the farmer has a total of 300 hours available, write a system of inequalities to represent the situation and graph it.

• x + y ≤ 250, 2x + y ≤ 200, x ≥ 0, y ≥ 0

• x + y ≤ 150, 2x + y ≤ 250, x ≥ 0, y ≥ 0

• The system of inequalities is: x + y ≤ 200, 2x + y ≤ 300, x ≥ 0, y ≥ 0.

• x + y ≤ 200, 2x + 2y ≤ 300, x ≥ 0, y ≥ 0

A school is organizing a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for food. Write an inequality to represent the maximum number of students that can attend the trip. Graph the inequality.

• x ≤ 20

• x ≤ 12

• x ≤ 10

• x ≤ 14

A factory produces two types of toys: A and B. Each toy A requires 3 hours of labor, and each toy B requires 2 hours. If the factory has 60 hours of labor available, write a system of inequalities to represent the production limits and graph it.

• 3x + 2y ≤ 60, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 60, x ≤ 0, y ≥ 0

• 3x + 2y ≤ 50, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≥ 0

A concert venue can hold a maximum of 500 people. If tickets are sold for $20 each, write an inequality to represent the maximum revenue the venue can earn if they want to keep ticket sales under $10,000. Graph the inequality.

• 20x < 10000, or x < 500

• 20x = 10000

• x > 500

• 20x > 10000

A bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery wants to make at least $100 in sales, write an inequality to represent the relationship between the number of cupcakes (x) and cookies (y) sold. Graph the inequality.

• 3x + 2y ≤ 100

• x + y ≥ 50

• 3x + 2y ≥ 100

• 5x + y ≥ 100

A student has a budget of $50 to spend on books and supplies. If each book costs $10 and each supply costs $5, write an inequality to represent the maximum number of books and supplies the student can buy. Graph the inequality.

• 3x + y ≤ 15

• x + 2y ≤ 20

• 2x + y ≤ 10

• 4x + y ≤ 12

A company produces two products, X and Y. Each product X requires 4 hours of production time, and each product Y requires 2 hours. If the company has 40 hours available, write a system of inequalities to represent the production limits and graph it.

• 2x + 4y ≤ 40, x ≥ 0, y ≥ 0

• The system of inequalities is: 4x + 2y ≤ 40, x ≥ 0, y ≥ 0.

• 3x + 4y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

A restaurant has a seating capacity of 120 people. If they want to maintain a ratio of at least 2:1 between tables for two and tables for four, write a system of inequalities to represent the seating arrangement and graph it.

• x + 2y ≤ 120, x ≤ 2y, x ≥ 0, y ≥ 0

• 3x + 4y ≤ 120, x ≥ 3y, x ≥ 0, y ≥ 0

• 2x + 4y ≤ 100, x ≥ y, x ≥ 0, y ≥ 0

• The system of inequalities is: 2x + 4y ≤ 120, x ≥ 2y, x ≥ 0, y ≥ 0.

A charity event aims to raise at least $1,000. If each ticket sold is $25 and each donation is $50, write an inequality to represent the relationship between the number of tickets (x) and donations (y) needed to meet the goal. Graph the inequality.

• 25x + 40y ≥ 1000

• 25x + 50y ≥ 1000

• 20x + 50y ≥ 1000

• 25x + 50y ≤ 1000