Real-World Linear Inequalities: Feasible Regions in Action

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x meters, what inequality represents the maximum area of the pen?

• 0 < x < 50

• x < 0

• 0 < x < 100

• 50 < x < 100

A school is planning a field trip and has a budget of $500. If each student ticket costs $15 and each adult ticket costs $20, what inequality can represent the number of tickets they can purchase?

• 15x + 20y < 500

• 15x + 20y ≤ 500

• 20x + 15y ≤ 500

• 10x + 15y ≤ 500

Maria wants to buy a new bike that costs $300. She has saved $150 and plans to save an additional $20 each week. Write an inequality to represent how many weeks it will take her to save enough money for the bike.

• 20w = 150

• 20w >= 150

• 20w <= 150

• 20w < 150

A gym has a maximum capacity of 200 members. If they currently have x members, write an inequality to represent how many more members they can accept.

• x = 200

• x > 200

• x ≤ 200

• x < 200

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student has $10 to spend, write an inequality to represent the maximum number of pencils and erasers they can buy if they buy at least 5 erasers.

• 0.50x + 1.00y < 10, y > 5

• 0.50x + 1.00y = 10, y = 5

• 0.50x + 1.00y <= 10, y >= 5

• 0.50x + 1.00y >= 10, y <= 5

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer has a budget of $50, write an inequality to represent the maximum number of miles they can drive.

• m ≤ 120

• m ≤ 90

• m ≤ 100

• m ≤ 80

A local theater has 300 seats. If they sell x tickets for a show, write an inequality to represent how many tickets can still be sold to reach full capacity.

• x <= 300

• x = 300

• x >= 300

• x < 300

A charity event aims to raise at least $1,000. If they have already raised $400 and plan to raise $50 each week, write an inequality to represent how many weeks it will take to reach their goal.

• w < 12

• w <= 10

• w >= 12

• w = 15

A pizza shop offers a deal where a large pizza costs $15 and a medium pizza costs $10. If a family wants to spend no more than $50, write an inequality to represent the number of large and medium pizzas they can buy.

• 15x + 10y ≤ 50

• 15x + 10y < 50

• 10x + 5y ≤ 50

• 5x + 20y ≤ 50

A student is saving for a new laptop that costs $800. If they currently have $200 and save $50 each month, write an inequality to determine how many months it will take to save enough for the laptop.

• m > 15

• m < 12

• m <= 10

• m >= 12