Inequalities in Action: Graphs & Word Problems for 9th Grade

A farmer has a budget of $200 to spend on seeds and fertilizer. Each bag of seeds costs $20 and each bag of fertilizer costs $30. Write a system of inequalities to represent the number of bags of seeds (x) and fertilizer (y) the farmer can buy. Graph the inequalities and interpret the feasible region.

• The system of inequalities is: 20x + 30y <= 200, x >= 0, y >= 0.

• 10x + 15y <= 200, x >= 0, y >= 0

• 25x + 35y <= 200, x >= 0, y >= 0

• 20x + 30y >= 200, x <= 0, y <= 0

A school is planning a field trip and has a maximum of 50 students who can attend. Each student costs $10 for transportation and $5 for food. Write a system of inequalities to represent the number of students (x) and the total cost (y). Graph the inequalities and explain the significance of the shaded area.

• x <= 30, y <= 20x

• x >= 50, y <= 10x

• x <= 50, y >= 15x

• x <= 50, y <= 15x

A gym offers two types of memberships: a basic membership for $25 per month and a premium membership for $40 per month. If a customer can spend no more than $200 on memberships, write a system of inequalities to represent the number of basic (x) and premium (y) memberships they can purchase. Graph the inequalities and describe the solution set.

• 25x + 40y ≥ 200, x ≤ 0, y ≤ 0

• 25x + 40y = 200, x ≥ 0, y ≥ 0

• The system of inequalities is: 25x + 40y ≤ 200, x ≥ 0, y ≥ 0.

• 30x + 35y ≤ 200, x ≥ 0, y ≥ 0

A company produces two products, A and B. Each product A requires 3 hours of labor and each product B requires 2 hours of labor. The company has a maximum of 30 hours of labor available. Write a system of inequalities to represent the number of products A (x) and B (y) that can be produced. Graph the inequalities and interpret the results.

• The system of inequalities is: 3x + 2y ≤ 30, x ≥ 0, y ≥ 0.

• x + y ≤ 30, x ≥ 0, y ≤ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 10

• 3x + 2y ≥ 30, x ≤ 0, y ≤ 0

A restaurant has a seating capacity of 100 people. Each table can seat 4 people. Write a system of inequalities to represent the number of tables (x) and the number of people (y) that can be seated. Graph the inequalities and explain the meaning of the feasible region.

• y = 4x + 10 and y = 100 - x

• The system of inequalities is: y <= 4x and y <= 100.

• y >= 4x and y >= 100

• y <= 2x and y <= 50

A local charity is organizing a fundraiser and has a goal of raising at least $500. Each ticket sold contributes $15. Write a system of inequalities to represent the number of tickets (x) sold and the total amount raised (y). Graph the inequalities and interpret the graph in the context of the fundraiser.

• y = 20x, y >= 500

• y = 10x, y >= 500

• y = 15x, y >= 500

• y = 15x, y < 500

A clothing store sells shirts for $15 and pants for $25. The store wants to make at least $300 in sales. Write a system of inequalities to represent the number of shirts (x) and pants (y) sold. Graph the inequalities and discuss the implications of the solution set.

• The system of inequalities is: 15x + 25y ≥ 300, x ≥ 0, y ≥ 0.

• 15x + 25y ≥ 250, x ≥ 0, y ≥ 0

• 15x + 25y ≤ 300, x ≥ 0, y ≥ 0

• 15x + 25y = 300, x ≥ 0, y ≥ 0

A student is saving money for a new laptop that costs $800. They can save $50 per week from their allowance and $20 per week from doing chores. Write a system of inequalities to represent the number of weeks (x) they need to save from allowance and chores (y). Graph the inequalities and analyze the feasible solutions.

• 50x + 20y <= 800, x >= 0, y >= 0

• 50x + 20y = 800, x >= 0, y >= 0

• 50x + 20y >= 1000, x >= 0, y >= 0

• The system of inequalities is: 50x + 20y >= 800, x >= 0, y >= 0.

A pet shelter has a limit of 40 animals they can take care of. Each dog takes up 2 spaces and each cat takes up 1 space. Write a system of inequalities to represent the number of dogs (x) and cats (y) the shelter can accommodate. Graph the inequalities and interpret the feasible region.

• 2x + y < 40, x > 0, y > 0

• x + 2y ≤ 40, x ≥ 0, y ≤ 40

• x + y ≤ 40, x ≥ 0, y ≥ 10

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

A student is planning to spend no more than $100 on books and supplies for school. Each book costs $20 and each supply pack costs $15. Write a system of inequalities to represent the number of books (x) and supply packs (y) they can buy. Graph the inequalities and explain the significance of the solution set.

• The system of inequalities is: 20x + 15y ≤ 100, x ≥ 0, y ≥ 0.

• 10x + 5y ≤ 100, x ≥ 0, y ≥ 0

• 20x + 15y = 100, x > 0, y > 0

• 20x + 15y ≥ 100, x ≤ 0, y ≤ 0