Graphing and Solving Linear Inequalities in Real Life

A farmer has 100 meters of fencing to create a rectangular pen. If the length of the pen is represented by x and the width by y, write the inequalities that represent the constraints on the dimensions of the pen. What are the possible dimensions?

• y < 0

• x + y ≥ 100

• x < 0

• The possible dimensions are defined by the inequalities: x + y ≤ 50, x > 0, y > 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 the inequalities that represent the number of students that can attend. How many students can they take if they want to maximize attendance?

• 10

• 20

• 14

• 12

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and gadget B requires 3 hours. If the company has 30 hours of labor available, write the inequality representing the production limits. What is the maximum number of gadgets they can produce?

• 15

• 25

• 10

• 20

A local gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium costs $50. If a customer wants to spend no more than $200 a month, write the inequality for the number of each type of membership they can purchase. What combinations are possible?

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

• (0, 5)

• (5, 0)

• (2, 3)

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs and each vanilla cake requires 2 eggs. If the bakery has 24 eggs, write the inequality for the number of cakes they can make. What is the maximum number of cakes they can produce?

• 10

• 15

• 8

• 12

A charity event is selling tickets for adults and children. Adult tickets cost $15 and children’s tickets cost $10. If the total revenue must be at least $300, write the inequality for the number of adult (x) and children (y) tickets sold. What combinations of tickets can meet this goal?

• 10x + 15y >= 300

• 15x + 10y >= 300

• 15x + 10y <= 300

• 20x + 5y >= 300

A car rental company has a fleet of 50 cars. They can rent out a maximum of 30 economy cars and 20 luxury cars. Write the inequalities that represent the rental limits. How many of each type of car can be rented out?

• Economy cars: 20, Luxury cars: 25

• Economy cars: 35, Luxury cars: 10

• Economy cars: 30, Luxury cars: 20

• Economy cars: 25, Luxury cars: 15

A restaurant has a special offer for lunch: a sandwich costs $5 and a drink costs $2. If a customer wants to spend no more than $20, write the inequality for the number of sandwiches (x) and drinks (y) they can buy. What are the possible combinations?

• 5x + 3y ≤ 20

• 5x + 2y ≤ 20

• 3x + 4y ≤ 20

• 2x + 5y ≤ 20

A clothing store has a sale on shirts and pants. Shirts cost $25 each and pants cost $40 each. If a customer has a budget of $200, write the inequality for the number of shirts (x) and pants (y) they can buy. What combinations fit within the budget?

• 30x + 35y ≤ 200

• 20x + 50y ≤ 200

• 25x + 40y < 200

• 25x + 40y ≤ 200

A concert venue has a seating capacity of 500. If they sell tickets for $30 for general admission and $50 for VIP, and they want to make at least $15,000, write the inequality for the number of general admission (x) and VIP (y) tickets sold. What combinations can achieve this revenue?

• x + y ≤ 500 and 30x + 50y ≥ 15000

• x + y ≤ 300 and 30x + 50y ≥ 20000

• x + y ≥ 500 and 30x + 50y ≤ 15000

• x + y = 500 and 30x + 50y = 10000