Inequalities in Real Life: Word Problems and Solutions

A school is planning a field trip and has a budget of $500. The cost per student is $20, and the bus rental is $200. Write a system of inequalities to represent the number of students that can attend the trip.

• 20x + 300 ≤ 500, x ≥ 0

• 15x + 200 ≤ 500, x ≥ 0

• 20x + 200 ≤ 500, x ≥ 0

• 25x + 200 ≤ 500, x ≥ 0

Maria has a budget of $150 to buy supplies for a community project. She wants to buy notebooks for $3 each and markers for $2 each. Write a system of inequalities to show how many notebooks and markers she can buy without exceeding her budget.

• 2x + 5y ≤ 150, x ≥ 0, y ≤ 0

• 3x + 2y ≤ 150, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 150, x ≥ 0, y ≥ 0

• 3x + 2y < 150, x ≥ 0, y ≥ 0

A farmer has 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If the farmer has 120 hours of labor available, write a system of inequalities to represent the planting options.

• x + y ≤ 120, 2x + y ≤ 100

• x + y ≤ 100, 2x + y ≤ 120

• x + 2y ≤ 100, 2x + y ≤ 100

• x + y ≤ 80, 2x + 3y ≤ 120

In a local gym, a fitness class can accommodate a maximum of 30 participants. Each participant pays $10, and the gym charges a flat fee of $100 for the class. Write a system of inequalities to represent the revenue generated from the class based on the number of participants.

• x <= 30, R >= 10x + 100

• x < 30, R <= 10x + 100

• x <= 20, R >= 10x + 200

• x >= 30, R = 10x + 50

A concert venue can hold a maximum of 500 people. Tickets are sold for $25 each, and VIP tickets are sold for $50 each. If the venue wants to make at least $10,000 from ticket sales, write a system of inequalities to represent the ticket sales.

• x + y ≤ 300, 25x + 50y ≥ 15000

• x + y ≤ 500, 25x + 50y ≥ 10000

• x + y ≤ 500, 25x + 50y = 5000

• x + y ≥ 500, 25x + 50y ≤ 10000

A bakery sells cookies for $1 each and cupcakes for $2 each. They want to make at least $100 in sales and can only produce a maximum of 80 items in total. Write a system of inequalities to represent the sales and production limits.

• 1x + 2y >= 80, x + y <= 100

• 1x + 2y = 100, x + y = 80

• 1x + 2y >= 100, x + y <= 80

• 1x + 2y <= 100, x + y >= 80

A charity organization is hosting a fundraiser. They need to raise at least $1,000. Each ticket sold is $15, and they have a maximum of 100 tickets available. Write a system of inequalities to represent the fundraising goal and ticket limit.

• 15x <= 1000, x >= 100

• 15x >= 1000, x <= 100

• 10x >= 1000, x <= 100

• 15x >= 500, x <= 50

A clothing store has a sale on shirts and pants. Shirts are $20 each, and pants are $30 each. They want to sell at least $500 worth of clothing and can only sell a maximum of 40 items. Write a system of inequalities to represent their sales goals.

• 15x + 25y ≥ 600, x + y ≤ 50

• 25x + 35y ≥ 500, x + y ≤ 30

• 10x + 20y ≥ 500, x + y ≤ 40

• 20x + 30y ≥ 500, x + y ≤ 40

A local theater has a seating capacity of 200. Regular tickets are $10, and premium tickets are $15. They want to earn at least $1,500 from ticket sales. Write a system of inequalities to represent the ticket sales and seating capacity.

• x + y ≤ 150, 10x + 15y ≥ 2000

• x + y ≥ 200, 10x + 15y ≤ 1500

• x + y < 200, 10x + 15y < 1500

• x + y ≤ 200, 10x + 15y ≥ 1500

A pet shelter has a maximum capacity of 50 animals. They currently have 20 dogs and want to adopt out at least 10 more. Write a system of inequalities to represent the number of dogs and the total capacity of the shelter.

• x >= 10, x + y >= 50

• x + y <= 60, x >= 0

• x <= 5, x + y <= 40

• x <= 10, x + y <= 50