Exploring Inequalities: Boundary Lines and Solutions

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. What is the boundary line for this inequality?

• x ≤ 14

• x ≤ 10

• x ≤ 12

• x ≤ 20

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 an inequality to represent the situation. Identify the boundary line.

• 2x + 3y ≤ 120; Boundary line: 2x + 3y = 120.

• x + y ≤ 240; Boundary line: x + y = 240.

• 2x + 3y ≤ 240; Boundary line: 2x + 3y = 240.

• 2x + 3y ≥ 240; Boundary line: 2x + 3y = 240.

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. What does the boundary line represent in this context?

• 25x ≤ 500, maximum number of students is 30.

• 15x ≤ 500, maximum number of students is 20.

• 20x < 500, maximum number of students is 24.

• 20x ≤ 500, maximum number of students is 25.

A bookstore sells novels for $15 each and textbooks for $25 each. If a customer wants to spend no more than $200, write an inequality to represent the number of novels (n) and textbooks (t) they can buy. Identify the boundary line for this inequality.

• 15n + 25t ≤ 200; Boundary line: 15n + 25t = 200

• 20n + 25t ≤ 200; Boundary line: 20n + 25t = 200

• 15n + 30t ≤ 200; Boundary line: 15n + 30t = 200

• 10n + 20t ≤ 200; Boundary line: 10n + 20t = 200

A concert venue has a seating capacity of 500. If tickets are sold for $30 each, write an inequality to represent the maximum number of tickets that can be sold without exceeding the capacity. What does the boundary line indicate?

• x ≥ 500; The boundary line indicates the total number of seats available.

• x = 500; The boundary line indicates the average attendance at the venue.

• x ≤ 500; The boundary line indicates the maximum capacity of the venue.

• x < 500; The boundary line indicates the minimum capacity of the venue.

A charity organization is collecting donations. They want to collect at least $1,000. If they have already collected $300, write an inequality to represent the additional amount they need to collect. Identify the boundary line for this situation.

• x <= 700

• x < 700

• x > 700

• x >= 700

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the miles driven. What is the boundary line for this inequality?

• m ≤ 150

• m ≤ 200

• m ≤ 300

• m ≤ 250

A pizza shop offers a deal where a large pizza costs $12 and each topping costs an additional $2. If a customer wants to spend no more than $30, write an inequality to represent the number of toppings they can add. Identify the boundary line.

• 12 + 2x ≥ 30; boundary line: x = 10

• 12 + 2x < 30; boundary line: x = 8

• 12 + 2x ≤ 30; boundary line: x = 9

• 12 + 2x = 30; boundary line: x = 9

A student is saving money for a new laptop that costs $800. If they currently have $200 and can save $50 each month, write an inequality to represent the number of months needed to save enough money. What does the boundary line represent?

• m >= 12

• m < 12

• m = 15

• m <= 10

A local park has a limit of 200 visitors at any given time. If a group of friends wants to have a picnic and they are bringing 15 people, write an inequality to represent the maximum number of additional visitors allowed. Identify the boundary line for this situation.

• x <= 185

• x <= 150

• x <= 200

• x <= 175