Solving Real-World Linear Inequalities: Grade 9 Challenges

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, what are the possible combinations of corn and wheat he can plant?

• (0, 100)

• Possible combinations of corn and wheat are: (0, 80), (10, 70), (20, 60), (30, 50), (40, 40), (50, 30), (60, 20), (70, 10), (80, 0).

• (20, 80)

• (90, 0)

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. If the school wants to take at least 20 students, what is the maximum number of students they can take on the trip?

• 15

• 30

• 0

• 25

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 4 hours of labor and each Type B gadget requires 2 hours. The company has 40 hours of labor available. If they want to produce at least 5 Type A gadgets, how many Type B gadgets can they produce?

• 15

• 10

• 5

• 20

A gym offers two types of memberships: Basic and Premium. The Basic membership costs $30 per month and the Premium membership costs $50 per month. If the gym wants to earn at least $1,200 in a month and has at least 20 Basic memberships sold, what is the maximum number of Premium memberships they can sell?

• 15

• 20

• 10

• 12

A concert hall has a seating capacity of 500. Tickets for the front row cost $50 and tickets for the back row cost $30. If the concert hall wants to earn at least $15,000 and sells at least 100 front row tickets, what is the maximum number of back row tickets they can sell?

• 450

• 300

• 400

• 250

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 and wants to make at least 10 chocolate cakes, how many vanilla cakes can they make?

• 5

• 20

• 10

• 15

A clothing store sells shirts and pants. Each shirt costs $25 and each pair of pants costs $40. If the store wants to make at least $1,000 in sales and sells at least 15 shirts, what is the maximum number of pairs of pants they can sell?

• 25

• 15

• 10

• 20

A charity organization is planning a fundraiser. They can sell tickets for $10 each or $15 each. If they want to raise at least $2,000 and sell at least 100 tickets, what is the maximum number of $15 tickets they can sell?

• 100

• 50

• 75

• 120

A pet store has a limit of 50 animals. They sell cats and dogs. Each cat costs $100 and each dog costs $200. If the store wants to make at least $8,000 in sales and has at least 10 cats, what is the maximum number of dogs they can sell?

• 30

• 40

• 25

• 15

A restaurant offers two types of meals: vegetarian and non-vegetarian. The vegetarian meal costs $12 and the non-vegetarian meal costs $18. If the restaurant wants to earn at least $1,500 and sells at least 50 vegetarian meals, what is the maximum number of non-vegetarian meals they can sell?

• 50

• 60

• 40

• 70