Graphing & Solving Real-World Inequalities for 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, how many acres of corn and wheat can he plant?

• 50 acres of corn and 50 acres of wheat

• 60 acres of corn and 40 acres of wheat

• 70 acres of corn and 30 acres of wheat

• 80 acres of corn and 20 acres of wheat

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. If the number of students is represented by x, write a system of inequalities to represent the situation and graph it.

• x >= 0 and x <= 14

• x >= 0 and x <= 20

• x >= 0 and x <= 5

• x >= 0 and x <= 10

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 wants to spend no more than $200 in a year, how many of each type of membership can they purchase?

• The customer can purchase up to 6 basic memberships, 4 premium memberships, or any combination that totals no more than $200.

• The customer can purchase 10 basic memberships and 1 premium membership.

• The customer can purchase 5 premium memberships.

• The customer can purchase 8 basic memberships.

A company produces two products, A and B. Each product A requires 3 hours of labor and each product B requires 2 hours of labor. The company has a maximum of 60 hours of labor available. Write a system of inequalities to represent the production limits and graph the feasible region.

• x + y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≤ 0

• The system of inequalities is: 3x + 2y ≤ 60, x ≥ 0, y ≥ 0.

• 3x + 2y ≥ 60, x ≤ 0, y ≤ 0

A concert hall can seat a maximum of 800 people. Tickets for adults cost $15 and tickets for children cost $10. If the total revenue from ticket sales must be at least $10,000, write a system of inequalities to represent the situation and interpret the results.

• x + y <= 800, 15x + 10y >= 10000

• x + y >= 800, 15x + 10y <= 10000

• x + y <= 600, 15x + 10y >= 12000

• x + y <= 800, 15x + 10y = 8000

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, how many cakes of each type can be made?

• 3 chocolate cakes and 4 vanilla cakes

• 2 chocolate cakes and 6 vanilla cakes

• 5 chocolate cakes and 0 vanilla cakes

• 4 chocolate cakes and 1 vanilla cake

A local charity is organizing a fundraiser. They plan to sell two types of items: T-shirts for $10 each and mugs for $5 each. If they want to raise at least $300, write a system of inequalities to represent the number of T-shirts and mugs they need to sell.

• 10x + 5y >= 300, x >= 0, y >= 0

• 5x + 10y >= 300, x >= 0, y >= 0

• 10x + 5y = 300, x >= 0, y >= 0

• 10x + 5y <= 300, x >= 0, y >= 0

A car rental company has a fleet of cars and trucks. Each car can be rented for $50 per day and each truck for $80 per day. If the company wants to earn at least $1,000 in a week, how many cars and trucks must they rent?

• At least 25 cars or 5 trucks

• At least 20 cars or 13 trucks, or any combination that satisfies 50c + 80t >= 1000.

• At least 30 cars or 8 trucks

• At least 15 cars or 10 trucks

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $12 and each non-vegetarian meal costs $15. If the restaurant wants to make at least $600 in a day, write a system of inequalities to represent the number of each type of meal they need to sell.

• 12x + 15y >= 600, x >= 0, y >= 0

• 12x + 10y >= 600, x >= 0, y >= 0

• 10x + 15y >= 600, x >= 0, y >= 0

• 12x + 15y <= 600, x >= 0, y >= 0

A clothing store has a sale on shirts and pants. Shirts are sold for $20 each and pants for $30 each. If the store wants to make at least $1,200 in sales, write a system of inequalities to represent the number of shirts and pants they need to sell.

• 10x + 20y >= 1200, x >= 0, y >= 0

• 25x + 35y >= 1200, x >= 0, y >= 0

• 20x + 30y >= 1200, x >= 0, y >= 0

• 15x + 25y >= 1200, x >= 0, y >= 0