Exploring Real-Life Linear Inequalities and Graphs

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost (C) for attending x classes in a month. Graph the inequality on a coordinate plane.

• C > 30 + 5x

• C <= 30 + 5x

• C = 30 + 5x

• C >= 30 + 5x

A farmer has 100 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 120 hours of labor available, write an inequality to represent the situation and graph it.

• x + y = 100, 2x + y = 120

• x + y ≥ 100, 2x + y ≥ 120

• x + y ≤ 120, 2x + y ≤ 100

• x + y ≤ 100, 2x + y ≤ 120

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write an inequality to represent the maximum number of students (s) that can attend the trip. Graph the inequality on a coordinate plane.

• s ≤ 25

• s ≤ 30

• s ≤ 20

• s < 25

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 60 hours of labor available, write an inequality to represent the production limits and graph it.

• 3x + 2y ≤ 60

• x + 2y ≤ 60

• 2x + 3y ≤ 60

• 3x + y ≤ 60

A concert venue can hold a maximum of 2000 people. If tickets are sold for $15 each, write an inequality to represent the total revenue (R) generated from selling t tickets. Graph the inequality on a coordinate plane.

• R ≤ 30000

• R ≥ 20000

• R = 15000

• R < 30000

A restaurant has a seating capacity of 150 people. If each table seats 5 people, write an inequality to represent the maximum number of tables (t) that can be set up. Graph the inequality on a coordinate plane.

• t >= 25

• t < 30

• t <= 30

• t > 30

A charity event aims to raise at least $1000. If each ticket sold is $25, write an inequality to represent the number of tickets (n) that need to be sold. Graph the inequality on a coordinate plane.

• n > 40

• n < 40

• n ≤ 40

• n ≥ 40

A student has a budget of $50 to spend on books. If each book costs $10, write an inequality to represent the maximum number of books (b) the student can buy. Graph the inequality on a coordinate plane.

• b < 5

• 10b >= 50

• 10b <= 50, b <= 5

• b <= 10

A factory produces two products: Product X and Product Y. Each Product X requires 4 hours of machine time, and each Product Y requires 2 hours. If the factory has 80 hours of machine time available, write an inequality to represent the production limits and graph it.

• 4x + 2y ≤ 80

• 4x + 3y ≤ 80

• 3x + 2y ≤ 80

• 2x + 4y ≤ 80

A sports team has a budget of $2000 for uniforms. If each uniform costs $50, write an inequality to represent the maximum number of uniforms (u) that can be purchased. Graph the inequality on a coordinate plane.

• u < 40

• u <= 40

• u >= 50

• u <= 30