Inequality Systems: Solving Real-World Problems in 9th Grade

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 3 hours of labor. If he has a total of 240 hours of labor available, write a system of inequalities to represent the situation and determine the maximum number of acres he can plant.

• 80

• 100

• 120

• 60

A school is organizing a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for food. Write a system of inequalities to represent the maximum number of students that can attend the trip, and solve for the number of students if the total cost must not exceed the budget.

• 10

• 14

• 12

• 18

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 situation and find the maximum number of each type of membership they can purchase.

• Maximum 4 basic memberships or 5 premium memberships.

• Maximum 7 basic memberships or 2 premium memberships.

• Maximum 6 basic memberships or 4 premium memberships.

• Maximum 5 basic memberships or 3 premium memberships.

A bakery produces 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 inequalities to represent the situation and determine how many cakes of each type can be made.

• The bakery can make a maximum of 5 vanilla cakes (0 chocolate) or 3 chocolate cakes and 4 vanilla cakes.

• The bakery can make 6 chocolate cakes (0 vanilla).

• The bakery can make 4 chocolate cakes and 5 vanilla cakes.

• The bakery can make 2 chocolate cakes and 8 vanilla cakes.

A concert hall has a seating capacity of 500. Tickets for the front row cost $50 each, and tickets for the back row cost $30 each. If the total revenue from ticket sales must be at least $15,000, write a system of inequalities to represent the situation and find the maximum number of tickets that can be sold for each row.

• Front row: 500, Back row: 500

• Front row: 300, Back row: 200

• Front row: 250, Back row: 250

• Front row: 400, Back row: 100

A clothing store sells shirts for $25 and pants for $40. The store has a budget of $1,000 for inventory. Write a system of inequalities to represent the maximum number of shirts and pants the store can purchase, and solve for the number of each type of clothing if they want to spend the entire budget.

• 30 shirts and 10 pants

• 40 shirts and 0 pants, or 0 shirts and 25 pants.

• 10 shirts and 20 pants

• 20 shirts and 15 pants

A charity event is selling tickets for $10 each and food for $5 each. They want to raise at least $1,000. Write a system of inequalities to represent the number of tickets and food items they need to sell to meet their goal, and determine the combinations that would work.

• x + y <= 100

• 3x + 2y >= 300

• The system of inequalities is: 2x + y >= 200, x >= 0, y >= 0. Combinations that work include (100, 0), (90, 20), (80, 40), (70, 60), (60, 80), (50, 100), etc.

• x + 2y >= 150

A local gym has a maximum capacity of 200 members. They offer a basic membership for $25 and a premium membership for $40. If they want to generate at least $6,000 in revenue, write a system of inequalities to represent the situation and find the maximum number of each type of membership they can sell.

• Maximum basic memberships: 200, Maximum premium memberships: 0

• Maximum basic memberships: 100, Maximum premium memberships: 100

• Maximum basic memberships: 150, Maximum premium memberships: 50

• Maximum basic memberships: 133, Maximum premium memberships: 67

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 they want to house at least 20 animals, write a system of inequalities to represent the situation and determine the maximum number of each type of animal they can have.

• 25 dogs and 5 cats

• 5 dogs and 45 cats

• 10 dogs and 30 cats

• 15 dogs and 20 cats

A restaurant has a seating capacity of 100. They serve two types of meals: a regular meal for $15 and a special meal for $25. If they want to make at least $1,500 in one night, write a system of inequalities to represent the situation and find the maximum number of each type of meal they can serve.

• Regular meals: 80, Special meals: 20

• Regular meals: 100, Special meals: 0

• Regular meals: 50, Special meals: 50

• Regular meals: 70, Special meals: 30