Mastering Linear Inequalities: Writing & Graphing Skills

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by x and the width by y, write a system of linear inequalities to represent the constraints on the dimensions of the pen. Graph the inequalities.

• x + y ≤ 50, x ≥ 0, y ≥ 0

• x + y ≥ 100

• y ≤ 0

• x ≤ 0

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 system of linear inequalities to represent the maximum number of students that can attend the trip. Graph the inequalities.

• x >= 0 and x <= 14

• x >= 0 and x <= 20

• x >= 5 and x <= 12

• x >= 0 and x <= 10

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours of baking time and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write a system of linear inequalities to represent the number of each type of cake that can be made. Graph the inequalities.

• x + 2y <= 10, x >= 0, y >= 0

• x + y <= 10, x >= 0, y <= 0

• The system of inequalities is: 2x + y <= 10, x >= 0, y >= 0.

• 2x + y >= 10, x >= 0, y >= 0

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month and the premium costs $50 per month. If a customer wants to spend no more than $200 a month, write a system of linear inequalities to represent the number of each type of membership they can purchase. Graph the inequalities.

• 30x + 50y ≤ 150, x ≥ 5, y ≥ 0

• The system of linear inequalities is: 30x + 50y ≤ 200, x ≥ 0, y ≥ 0.

• 30x + 50y = 200, x ≥ 0, y ≤ 0

• 30x + 50y ≥ 200, x ≤ 0, y ≤ 0

A company produces two products, A and B. Each product A requires 3 hours of labor and each product B requires 2 hours. If the company has a total of 24 hours of labor available, write a system of linear inequalities to represent the production limits. Graph the inequalities.

• 4x + 2y ≤ 24, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 24, x ≥ 0, y ≥ 0

• 3x + y ≤ 24, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 24, x ≥ 0, y ≥ 0

A concert hall has a seating capacity of 300. Tickets for the front row cost $50 and tickets for the back row cost $30. If the total revenue from ticket sales must be at least $10,000, write a system of linear inequalities to represent the ticket sales. Graph the inequalities.

• x + y ≤ 300, 50x + 30y ≥ 10000

• x + y ≥ 300, 50x + 30y ≤ 10000

• x + y = 300, 50x + 30y = 10000

• x + y ≤ 250, 50x + 30y ≥ 12000

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. If a customer has a budget of $200, write a system of linear inequalities to represent the maximum number of shirts and pants they can buy. Graph the inequalities.

• The system of linear inequalities is: 20x + 30y ≤ 200, x ≥ 0, y ≥ 0.

• 20x + 30y = 200, x ≥ 0, y ≤ 0

• 20x + 30y ≥ 200, x ≤ 0, y ≤ 0

• 10x + 15y ≤ 200, x ≥ 0, y ≥ 0

A charity event is selling tickets for a dinner. Each ticket costs $25 and the goal is to raise at least $1,000. Write a system of linear inequalities to represent the number of tickets that need to be sold. Graph the inequalities.

• x = 40

• x > 50

• x <= 30

• x >= 40

A student is planning to study for two subjects: Math and Science. Each hour spent on Math is worth 2 points and each hour spent on Science is worth 3 points. If the student wants to earn at least 12 points in total, write a system of linear inequalities to represent the study hours. Graph the inequalities.

• The system of linear inequalities is: { 2x + 3y >= 12, x >= 0, y >= 0 }.

• 2x + 3y <= 12, x >= 0, y >= 0

• x + y >= 12, x >= 0, y >= 0

• 2x + 3y >= 10, x >= 0, y >= 0

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $10 and each non-vegetarian meal costs $15. If the restaurant wants to make at least $300 in a day, write a system of linear inequalities to represent the number of each type of meal that must be sold. Graph the inequalities.

• x + y <= 20

• 5x + 10y >= 300

• 10x + 20y >= 300

• 10x + 15y >= 300, x >= 0, y >= 0