Mastering Systems of Inequalities: Graphing & Writing Skills

A farmer has 100 meters of fencing to create a rectangular pen for sheep. The length of the pen must be at least 10 meters. Write a system of inequalities to represent the possible dimensions of the pen.

• L + W ≤ 60, L ≥ 15

• L + W < 50, L ≥ 5

• L + W ≤ 50, L ≥ 10

• L + W = 100, L ≥ 10

A school is planning a field trip and has a budget of $500. Each student ticket costs $15, and each adult ticket costs $20. Write a system of inequalities to represent the number of student and adult tickets they can purchase without exceeding the budget.

• 20x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 15x + 25y ≤ 500, x ≥ 0, y ≥ 0

• 10x + 15y ≤ 500, x ≥ 0, y ≥ 0

• 15x + 20y ≤ 500, x ≥ 0, y ≥ 0

A bakery sells two types of cakes: chocolate and vanilla. The bakery can make a maximum of 50 cakes in a day. They want to make at least 10 chocolate cakes. Write a system of inequalities to represent the number of chocolate and vanilla cakes they can bake.

• x + y = 50, y >= 10

• x + y >= 50, x <= 10

• x + y <= 40, x >= 5

• x + y <= 50, x >= 10

A gym has a maximum capacity of 200 members. They currently have 50 members. If they want to maintain at least 30 new members, write a system of inequalities to represent the number of new members they can accept.

• n >= 30 and n <= 200

• n >= 0 and n <= 200

• n >= 50 and n <= 100

• n >= 30 and n <= 150

A concert hall has 300 seats. Tickets for adults cost $30, and tickets for children cost $15. If the total revenue from ticket sales must be at least $6000, write a system of inequalities to represent the number of adult and child tickets sold.

• x + y ≤ 300, 30x + 15y ≥ 6000

• x + y ≥ 300, 30x + 15y ≤ 6000

• x + y = 300, 30x + 15y = 6000

• x + y ≤ 250, 30x + 15y ≥ 5000

A local charity is organizing a food drive. They want to collect at least 200 cans of food and have a maximum of 500 cans they can store. Write a system of inequalities to represent the number of cans they can collect.

• x = 300

• x > 500

• 200 <= x <= 500

• x < 200

A company produces two products, A and B. Each product A requires 2 hours of labor, and each product B requires 3 hours. The company has a maximum of 30 hours of labor available per week. Write a system of inequalities to represent the number of products A and B they can produce.

• 2x + y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≥ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• x + y ≤ 30, x ≥ 0, y ≥ 0

A restaurant has a seating capacity of 100 people. They want to serve at least 20 children and have a maximum of 40 adults. Write a system of inequalities to represent the number of children and adults they can serve.

• c + a >= 100, c <= 20, a >= 40

• c + a <= 80, c >= 10, a <= 50

• c + a <= 100, c >= 20, a <= 40

• c + a = 100, c <= 20, a >= 40

A clothing store has a sale on shirts and pants. They have a total of 80 items to sell, and they want to sell at least 10 shirts. Write a system of inequalities to represent the number of shirts and pants they can sell.

• x + y ≤ 80, x ≥ 10

• x + y ≥ 80, y ≥ 10

• x + y < 80, x ≤ 10

• x + y = 80, x = 5

A community center is hosting a workshop and can accommodate a maximum of 50 participants. They want to ensure that at least 15 participants are adults. Write a system of inequalities to represent the number of adults and children that can attend the workshop.

• x + y = 50, x ≤ 10

• x + y ≤ 50, x ≥ 15

• x + y ≥ 50, y ≤ 35

• x + y < 50, x < 15