Mastering Graphing Linear Inequalities: Real-World Problems

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write a linear inequality to represent the total cost for attending classes, and graph it for up to 10 classes.

• C <= 30 + 10x, for 0 <= x <= 10

• C < 30 + 5x, for 0 <= x <= 5

• C >= 30 + 5x, for 0 <= x <= 10

• C <= 30 + 5x, for 0 <= x <= 10

A farmer has a budget of $200 to buy seeds for two types of crops. If type A seeds cost $10 per bag and type B seeds cost $15 per bag, write a linear inequality to represent the budget constraint and graph it.

• 5x + 10y ≤ 200

• 15x + 10y ≤ 200

• 10x + 20y ≤ 200

• 10x + 15y ≤ 200

A school is planning a field trip and has a budget of $500. If each student pays $25, write a linear inequality to represent the maximum number of students that can attend, and graph it.

• x ≤ 15

• x ≤ 25

• x ≤ 10

• x ≤ 20

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear inequality to represent the total cost for driving up to 200 miles, and graph it.

• C <= 50 + 0.20x, 0 <= x <= 200

• C >= 50 + 0.20x, 0 <= x <= 200

• C <= 50 + 0.20x, 0 <= x <= 100

• C <= 50 + 0.50x, 0 <= x <= 200

A concert venue can hold a maximum of 500 people. If tickets are sold for $20 each, write a linear inequality to represent the total revenue generated from ticket sales, and graph it.

• R = 20x, where x < 500

• R < 20x, where x = 600

• R >= 20x, where x <= 300

• R <= 20x, where x <= 500

A bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make at least $100 in sales, write a linear inequality to represent the sales requirement and graph it.

• x + 2y >= 100

• 2x + y <= 100

• 2x + y >= 100

• 3x + y >= 100

A student has a part-time job and can work a maximum of 15 hours a week. If they earn $10 per hour, write a linear inequality to represent their weekly earnings, and graph it.

• E < 150

• E = 150

• E <= 150

• E >= 150

A company produces two products, A and B. Each product A requires 3 hours of labor and each product B requires 2 hours. If the company has a maximum of 60 hours available, write a linear inequality to represent the production limit and graph it.

• 3x + 2y ≥ 60

• 3x + 2y ≤ 60

• 2x + 3y ≤ 60

• 4x + y ≤ 60

A charity event aims to raise at least $1,000. If each ticket sold is $25, write a linear inequality to represent the number of tickets that need to be sold, and graph it.

• t < 40

• t <= 40

• t >= 40

• t > 40

A student is saving money for a new laptop that costs $800. If they save $50 each week, write a linear inequality to represent the number of weeks needed to save enough money, and graph it.

• 50w >= 800

• 50w <= 800

• 50w = 800

• 50w < 800