Exploring Linear Inequalities: Real-Life Applications

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 a linear inequality to represent the number of classes they can attend. Solve the inequality and graph the solution.

• x ≤ 10

• x ≤ 12

• x ≤ 20

• x ≤ 14

A school is planning a field trip and has a budget of $500. The cost per student is $20. Write a linear inequality to determine how many students can attend the trip without exceeding the budget. Solve the inequality and graph the solution.

• x ≤ 20

• x < 25

• x ≤ 25

• x ≤ 30

A farmer has 120 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 3 hours. If the farmer has a maximum of 240 hours of labor available, write a linear inequality to represent the situation. Solve and graph the inequality.

• 4x + 2y ≤ 240

• x + y ≤ 120

• 2x + 3y ≥ 240

• 2x + 3y ≤ 240

A company produces t-shirts and hoodies. Each t-shirt requires 2 hours of labor, and each hoodie requires 3 hours. If the company has 60 hours of labor available, write a linear inequality to represent the maximum number of t-shirts and hoodies that can be produced. Solve and graph the inequality.

• 3x + 2y ≤ 60

• x + 2y ≤ 60

• 2x + 3y ≤ 60

• 2x + 3y = 60

A student has a budget of $50 to spend on school supplies. If notebooks cost $3 each and pens cost $2 each, write a linear inequality to represent the number of notebooks and pens the student can buy. Solve the inequality and graph the solution.

• 3x + 2y < 50

• 3x + 2y ≤ 50

• 2x + 5y ≤ 50

• 4x + 3y ≤ 50

A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If a customer wants to spend no more than $100, write a linear inequality to represent the miles they can drive. Solve the inequality and graph the solution.

• m <= 240

• m <= 200

• m <= 180

• m <= 300

A bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make at least $100 in one day, write a linear inequality to represent the number of cupcakes and cookies they need to sell. Solve and graph the inequality.

• 2x + y ≥ 100

• 3x + 2y ≤ 100

• x + 2y ≥ 100

• x + y ≥ 100

A charity event has a goal of raising 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 to meet the goal. Solve the inequality and graph the solution.

• x >= 40

• x > 40

• x <= 40

• x < 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. Solve the inequality and graph the solution.

• w < 16

• w >= 16

• w > 16

• w <= 16