Inequalities in Action: Writing & Analyzing Solutions

A farmer has 100 acres of land. He wants 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 he has a total of 120 hours of labor available, write a system of inequalities to represent the situation. What are the possible combinations of corn and wheat he can plant?

• x + y ≤ 120, 2x + y ≤ 100

• x + y ≤ 100, 2x + y ≤ 120

• x + 2y ≤ 100, 2x + 2y ≤ 120

• x + y ≤ 80, 2x + y ≤ 100

A school is organizing 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 inequalities to represent the maximum number of students that can attend the trip. Analyze the solutions to determine how many students can go if the school wants to spend at least $300.

• 5 to 10 students can go on the trip.

• 1 to 7 students can go on the trip.

• 15 to 20 students can go on the trip.

• 8 to 14 students can go on the trip.

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer can spend no more than $200 per month on memberships, write a system of inequalities to represent the number of basic and premium memberships they can purchase. What combinations of memberships are possible?

• (0, 5)

• (2, 3)

• (5, 0)

• Possible combinations of memberships are: (0, 4), (1, 3), (2, 2), (3, 1), (4, 0) for (basic, premium) respectively.

A concert hall has a seating capacity of 500. Tickets for the front row are $50 each, and tickets for the back row are $30 each. If the total revenue from ticket sales must be at least $15,000, write a system of inequalities to represent the number of tickets sold for each row. What combinations of tickets meet the revenue requirement?

• x + y <= 500, 50x + 30y = 15000

• x >= 0, y <= 500 - x, 50x + 30y >= 15000

• x <= 0, y >= 500 - x, 50x + 30y <= 15000

• x >= 500, y >= 0, 50x + 30y >= 20000

A local gym has a maximum capacity of 200 members. Each membership costs $25 per month. If the gym wants to earn at least $3,000 in membership fees, write a system of inequalities to represent the number of members they can have. What are the possible numbers of members that meet the revenue goal?

• 120 <= x <= 200

• 0 <= x <= 200

• 50 <= x <= 150

• 100 <= x <= 250

A charity event is selling tickets for $10 each and has a goal of raising at least $1,000. If they can sell no more than 150 tickets, write a system of inequalities to represent the ticket sales. Analyze the solutions to find the range of tickets that can be sold to meet the fundraising goal.

• 100 <= x <= 150

• 50 <= x <= 100

• x < 100

• x > 150

A pet store has a limit of 50 animals it can house. They have dogs and cats, with each dog taking up 2 spaces and each cat taking up 1 space. If the store wants to have at least 10 dogs, write a system of inequalities to represent the situation. What combinations of dogs and cats can the store accommodate?

• d + c <= 50, d >= 5

• 2d + c >= 50, d <= 10

• 2d + c <= 40, d >= 15

• The system of inequalities is: 2d + c <= 50, d >= 10. Possible combinations are: (10, 30), (11, 28), (12, 26), (13, 24), (14, 22), (15, 20), (16, 18), (17, 16), (18, 14), (19, 12), (20, 10), (21, 8), (22, 6), (23, 4), (24, 2), (25, 0).

A school is planning a sports day and has a budget of $1,200. They need to rent equipment that costs $200 per set and pay for refreshments that cost $5 per student. Write a system of inequalities to represent the maximum number of equipment sets and students they can afford. Analyze the solutions to determine how many students can participate if they want to rent at least 3 sets of equipment.

• 120

• 90

• 100

• 150