Real-Life Linear Inequalities: Graphing & Word Problems

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. Graph the inequality.

• x ≤ 10

• x ≤ 20

• x ≤ 12

• x ≤ 14

A farmer has 200 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 1 hour. If the farmer has a total of 300 hours of labor available, write a linear inequality to represent the situation and graph it.

• x + y ≤ 200, 2x + y ≤ 300

• x + y ≤ 150, 2x + y ≤ 250

• x + y ≤ 200, 2x + y = 300

• x + y ≥ 200, 2x + y ≥ 300

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write a linear inequality to represent the maximum number of students that can attend the trip. Graph the inequality.

• 25x ≤ 500, x ≤ 20

• 40x ≤ 500, x ≤ 12

• 35x ≤ 500, x ≤ 14

• 30x ≤ 500, x ≤ 10

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor, and each Type B gadget requires 2 hours. If the company has 60 hours of labor available, write a linear inequality to represent the production limits and graph it.

• 3x + 2y ≥ 60

• 2x + 3y ≤ 60

• 4x + y ≤ 60

• 3x + 2y ≤ 60

A restaurant sells two types of sandwiches: vegetarian and meat. The vegetarian sandwich costs $5, and the meat sandwich costs $7. If the restaurant wants to make at least $200 in a day, write a linear inequality to represent the number of each type of sandwich they need to sell. Graph the inequality.

• 6x + 5y ≥ 200

• 3x + 4y ≥ 200

• 5x + 7y ≤ 200

• 5x + 7y ≥ 200

A student has a budget of $50 to spend on books. If each textbook costs $15 and each novel costs $10, write a linear inequality to represent the number of textbooks and novels the student can buy. Graph the inequality.

• 20x + 10y ≤ 50

• 5x + 5y ≤ 50

• 10x + 15y ≤ 50

• 15x + 10y ≤ 50

A concert venue has a seating capacity of 500. If tickets for the front row cost $50 and tickets for the back row cost $30, and the venue wants to make at least $15,000 from ticket sales, write a linear inequality to represent the ticket sales. Graph the inequality.

• 50x + 30y ≥ 15000, x + y ≤ 500

• 50x + 30y ≥ 20000, x + y ≤ 400

• 50x + 30y = 15000, x + y = 500

• 50x + 30y ≤ 15000, x + y ≥ 500

A clothing store sells shirts for $20 and pants for $30. If the store wants to make at least $1,000 in sales, write a linear inequality to represent the number of shirts and pants that need to be sold. Graph the inequality.

• 2x + 3y ≥ 100

• x + y ≥ 100

• 2x + 3y = 100

• 2x + 3y ≤ 100

A charity event is selling tickets for $25 each and wants to raise at least $2,000. Write a linear inequality to represent the number of tickets that need to be sold. Graph the inequality.

• 25x <= 2000

• x <= 80

• 25x = 2000

• 25x >= 2000, x >= 80

A bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery wants to earn at least $150 in one day, write a linear inequality to represent the number of cupcakes and cookies they need to sell. Graph the inequality.

• 4x + y ≥ 150

• 3x + 2y < 150

• 3x + 2y ≥ 150

• x + 3y ≥ 150