Inequality Statements in Real-World Scenarios: Grade 9 Quiz

A farmer has a total of 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 and determine the maximum number of acres he can plant.

• 40 acres of corn and 20 acres of wheat

• 70 acres of corn and 10 acres of wheat

• 60 acres of corn and 0 acres of wheat

• 50 acres of corn and 25 acres of wheat

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 while staying within budget.

• x ≤ 14

• x ≤ 20

• x ≤ 10

• x ≤ 12

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.

• 30x + 50y >= 200, x >= 0, y >= 0

• 30x + 50y <= 150, x >= 0, y >= 0

• 20x + 40y <= 200, x >= 0, y >= 0

• 30x + 50y <= 200, x >= 0, y >= 0

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 number of front and back row tickets sold.

• x + y <= 400, 50x + 30y >= 20000

• x + y >= 500, 50x + 30y <= 15000

• x + y = 500, 50x + 30y = 15000

• x + y <= 500, 50x + 30y >= 15000

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 60 eggs available, write a system of inequalities to represent the number of each type of cake that can be made.

• 4x + y <= 60, x >= 0, y >= 0

• 2x + 3y <= 60, x >= 0, y >= 0

• 3x + 2y <= 60, x >= 0, y >= 0

• 3x + 3y <= 60, x >= 0, y >= 0

A company produces two products, A and B. Each product A requires 4 hours of labor and each product B requires 2 hours of labor. If the company has a total of 40 hours of labor available, write a system of inequalities to represent the production limits for products A and B.

• 4x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 5x + y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 4y ≤ 40, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 40, x ≥ 0, y ≥ 0

A local gym has a maximum capacity of 150 members. If they currently have 80 members and plan to add both individual and family memberships, where each individual membership is for 1 person and each family membership is for 4 people, write a system of inequalities to represent the maximum number of each type of membership they can add.

• x + 4y <= 100, x >= 0, y >= 0

• x + 4y <= 70, x >= 0, y >= 0

• x + 4y <= 80, x >= 0, y >= 0

• x + 4y <= 60, x >= 0, y >= 1

A charity event is selling tickets for $10 each and is aiming to raise at least $1,000. If they also have a goal of selling no more than 150 tickets, write a system of inequalities to represent the ticket sales situation.

• 10x ≤ 1000, x ≤ 100

• 10x < 1000, x > 150

• 10x ≥ 500, x ≤ 200

• 10x ≥ 1000, x ≤ 150

A restaurant has a maximum seating capacity of 200. If they have 50 tables and each table can seat either 4 or 6 people, write a system of inequalities to represent the possible combinations of tables that can be used to maximize seating without exceeding capacity.

• x + y <= 100, 4x + 6y <= 300, x >= 0, y >= 0

• x + y <= 50, 4x + 6y <= 150, x >= 0, y >= 0

• x + y <= 50, 4x + 6y <= 250, x >= 0, y >= 0

• x + y <= 50, 4x + 6y <= 200, x >= 0, y >= 0

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1,000 in sales and can only sell a maximum of 50 items, write a system of inequalities to represent the sales goals for shirts and pants.

• 25x + 40y ≤ 1000, x + y ≥ 50

• 30x + 35y ≥ 1000, x + y ≤ 50

• 25x + 40y = 1000, x + y = 50

• 25x + 40y ≥ 1000, x + y ≤ 50