Graphing and Interpreting Linear Inequalities for Grade 9

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write a linear inequality to represent the total cost (C) for attending x classes if you want to spend no more than $100. Graph the inequality and interpret the graph.

• C = 30 + 5x; 30 + 5x ≥ 100; x ≥ 14

• C = 30 + 5x; 30 + 5x ≤ 50; x ≤ 4

• C = 30 + 5x; 30 + 5x ≤ 100; x ≤ 14

• C = 30 + 10x; 30 + 10x ≤ 100; x ≤ 7

A school is planning a field trip and has a budget of $500. The cost per student is $20, and there are additional costs of $100 for transportation. Write a linear inequality to represent the maximum number of students (s) that can attend. Graph the inequality and interpret the results.

• s < 20

• s <= 20

• s >= 25

• s + 100 <= 500

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 limits. Graph the inequality and describe the feasible production combinations.

• 2x + 3y ≤ 30

• 2x + 3y ≥ 30

• x + y ≤ 10

• 2x + 3y = 30

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs, and each vanilla cake requires 2 eggs. If the bakery has 60 eggs, write a linear inequality to represent the number of cakes that can be made. Graph the inequality and explain the feasible combinations of cakes.

• 2x + 5y ≤ 60

• 4x + 3y ≤ 60

• 3x + 2y < 60

• 3x + 2y ≤ 60

A charity event aims to raise at least $2000. If each ticket sold is $50 and there are additional donations of $500, write a linear inequality to represent the number of tickets (t) that need to be sold. Graph the inequality and interpret the graph.

• t ≥ 30

• t > 30

• t ≤ 30

• t < 30

A student has a budget of $150 to spend on books and supplies. If each book costs $25 and each supply costs $10, write a linear inequality to represent the maximum number of books (b) and supplies (s) that can be purchased. Graph the inequality and describe the feasible combinations.

• 30b + 5s ≤ 150

• 20b + 15s ≤ 150

• 10b + 20s ≤ 150

• 25b + 10s ≤ 150

A restaurant has a maximum of 100 seats. If each table seats 4 people, write a linear inequality to represent the number of tables (t) that can be set up. Graph the inequality and interpret the graph in terms of seating capacity.

• t ≤ 15

• t ≤ 30

• t ≤ 20

• t ≤ 25

A clothing store has a sale where jeans cost $30 each and shirts cost $20 each. If a customer wants to spend no more than $200, write a linear inequality to represent the number of jeans (j) and shirts (s) that can be purchased. Graph the inequality and explain the feasible combinations.

• 30j + 25s ≤ 200

• 25j + 15s ≤ 200

• 30j + 20s ≤ 200

• 40j + 10s ≤ 200