Inequality Interpretations: Real-Life Scenarios for 9th Graders

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 an inequality to represent the number of classes they can attend. Graph the inequality and interpret the solution.

• x ≤ 12

• x ≤ 10

• x ≤ 14

• x ≤ 20

A farmer has 200 feet of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write an inequality that represents the maximum area he can enclose. Graph the inequality and explain the feasible solutions.

• The inequality representing the maximum area is x + y ≤ 100, x ≥ 0, y ≥ 0.

• x + y ≤ 50, x ≥ 0, y ≥ 0

• x + y ≤ 200, x ≥ 0, y ≥ 0

• x + y ≤ 150, x ≥ 0, y ≥ 0

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 that can attend the trip. Graph the inequality and interpret the results.

• x ≤ 30

• x ≤ 20

• x ≤ 25

• x ≤ 15

A factory produces widgets and has a maximum production capacity of 300 units per day. If the factory produces x units of type A and y units of type B, write an inequality to represent the production limit. Graph the inequality and discuss the possible combinations of widgets produced.

• x + y = 300

• x + y ≤ 300

• x + y ≥ 300

• x + y < 300

A concert venue has a seating capacity of 800. If tickets are sold for $15 each, write an inequality to represent the total revenue generated if x tickets are sold. Graph the inequality and interpret the solution in terms of revenue.

• 15x <= 12000

• 10x <= 8000

• 20x >= 16000

• 15x < 12000

A student is saving money for a new laptop that costs $800. If they save $50 each week, write an inequality to represent the number of weeks needed to save enough money. Graph the inequality and interpret the solution in the context of their savings plan.

• w < 16

• w >= 16

• w > 16

• w <= 16

A restaurant has a maximum capacity of 120 customers. If they have x tables for two and y tables for four, write an inequality to represent the seating arrangement. Graph the inequality and discuss the possible seating combinations.

• 2x + 4y < 120

• 3x + 2y ≤ 120

• 2x + 4y ≤ 120

• x + y ≤ 60

A charity event aims to raise at least $1,000. If each ticket sold is $25, write an inequality to represent the number of tickets that need to be sold. Graph the inequality and interpret the solution in terms of ticket sales.

• x < 40

• x > 40

• x >= 40

• x <= 40