Graphing and Interpreting Linear Inequalities in Real Life

A local bakery sells cupcakes and cookies. Each cupcake costs $2 and each cookie costs $1. If the bakery wants to make at least $50 in one day, write a linear inequality to represent the number of cupcakes (x) and cookies (y) they need to sell. Graph the inequality and interpret the solution.

• x + y ≥ 50

• 3x + 2y ≤ 50

• 2x + y ≥ 50

• x + 2y ≥ 50

A school is planning a field trip and has a budget of $300. The cost per student is $15 for the trip. Write a linear inequality to represent the number of students (x) that can attend the trip. Graph the inequality and explain what the solution means in the context of the trip.

• 20x <= 300

• x < 15

• 10x <= 300

• 15x <= 300, x <= 20

A 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 for the number of classes (y) they can attend. Graph the inequality and interpret the results.

• y ≤ 14

• y ≤ 12

• y ≤ 20

• y ≤ 10

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. If the farmer has 120 hours of labor available, write a linear inequality to represent the situation. Graph the inequality and discuss the feasible solutions.

• 2x + y >= 120 and x + y >= 100

• The linear inequalities are: 2x + y <= 120 and x + y <= 100.

• x + 2y <= 120 and x + y <= 100

• 2x + y <= 100 and x + y <= 120

A concert venue has a seating capacity of 500. If tickets for the concert are sold at $20 each and VIP tickets at $50 each, and the venue wants to make at least $10,000, write a linear inequality for the number of regular tickets (x) and VIP tickets (y) sold. Graph the inequality and interpret the solution.

• The linear inequalities are: x + y ≤ 500 and 20x + 50y ≥ 10000.

• x + y ≥ 500 and 20x + 50y ≤ 10000

• x + y = 500 and 20x + 50y = 10000

• x + y ≤ 300 and 20x + 50y ≥ 5000

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1,000 in sales, write a linear inequality to represent the number of shirts (x) and pants (y) sold. Graph the inequality and explain the significance of the solution.

• 25x + 40y ≥ 1000

• 30x + 35y ≥ 1000

• 25x + 40y ≤ 1000

• 20x + 50y ≥ 1000

A charity organization is hosting a fundraiser and has a goal of raising at least $2,000. If they charge $10 per ticket and $50 for a table of 5 tickets, write a linear inequality for the number of individual tickets (x) and tables (y) sold. Graph the inequality and interpret the results.

• 15x + 40y ≥ 2000

• 10x + 50y ≤ 2000

• 10x + 50y ≥ 2000

• 5x + 25y ≥ 2000

A tech company produces laptops and tablets. Each laptop requires 3 hours of assembly, and each tablet requires 2 hours. If the company has 60 hours available for assembly, write a linear inequality for the number of laptops (x) and tablets (y) produced. Graph the inequality and discuss the implications of the solution.

• 3x + 2y ≤ 60

• 4x + y ≤ 60

• x + 4y ≤ 60

• 2x + 3y ≤ 60

A restaurant offers a special deal on burgers and fries. Each burger costs $5 and each order of fries costs $2. If the restaurant wants to earn at least $200 in one day, write a linear inequality for the number of burgers (x) and fries (y) sold. Graph the inequality and interpret the solution.

• 4x + y = 200

• 5x + 2y ≥ 200

• 6x + 3y ≥ 250

• 3x + 4y ≤ 150

A community center has a budget of $1,500 for a summer camp. Each child costs $100 to enroll, and each additional activity costs $20 per child. Write a linear inequality to represent the number of children (x) and activities (y) that can be offered. Graph the inequality and explain the meaning of the solution.

• 100x + 20y ≤ 1500

• 100x + 20y ≥ 1500

• 50x + 10y ≤ 1500

• 200x + 30y ≤ 1500