Writing and Solving Linear Inequalities in Real Life

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 1 hour of labor. If he has a total of 120 hours of labor available, write a system of inequalities to represent the situation. What are the possible combinations of corn and wheat he can plant?

• x + y = 100, 2x + y = 120

• x + y <= 80, 2x + y <= 100

• x + y >= 100, 2x + y >= 120

• x + y <= 100, 2x + y <= 120

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. Write a system of inequalities to represent the maximum number of students that can attend the trip. How many students can they take if they want to spend less than the budget?

• 10

• 18

• 12

• 14

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of assembly, and each Type B gadget requires 2 hours. The company has a maximum of 30 hours available for assembly. Write a system of inequalities to represent the production limits. How many of each type can they produce?

• The company can produce a maximum of 20 Type A gadgets (0 Type B) or 5 Type B gadgets (0 Type A).

• The company can produce a maximum of 8 Type A gadgets and 10 Type B gadgets.

• The company can produce a maximum of 12 Type A gadgets and 6 Type B gadgets simultaneously.

• The company can produce a maximum of 10 Type A gadgets (0 Type B) or 15 Type B gadgets (0 Type A), or any combination that satisfies 3x + 2y ≤ 30.

A gym has a maximum capacity of 200 members. Each membership costs $30 per month. If the gym wants to earn at least $5000 per month, write a system of inequalities to represent the situation. What is the minimum number of members needed to meet the revenue goal?

• 200

• 150

• 167

• 180

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 cups of flour, and each vanilla cake requires 3 cups. If the bakery has 30 cups of flour, write a system of inequalities to represent the number of cakes they can bake. How many cakes of each type can they make?

• 5 chocolate cakes and 5 vanilla cakes

• 12 vanilla cakes and 3 chocolate cakes

• 8 chocolate cakes and 4 vanilla cakes

• The bakery can make a maximum of 10 vanilla cakes and 0 chocolate cakes, or 0 vanilla cakes and 15 chocolate cakes.

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 from ticket sales, write a system of inequalities to represent the ticket sales. What are the possible combinations of front and back row tickets sold?

• x + y ≥ 500, 50x + 30y ≤ 15000

• x + y ≤ 300, 50x + 30y ≥ 20000

• x + y = 500, 50x + 30y = 10000

• x + y ≤ 500, 50x + 30y ≥ 15000

A clothing store sells shirts and pants. Each shirt costs $20, and each pair of pants costs $30. The store has a budget of $600 for inventory. Write a system of inequalities to represent the maximum number of shirts and pants the store can buy. How many of each can they purchase?

• 10 shirts and 15 pants

• The store can purchase a maximum of 30 shirts and 0 pants, or 0 shirts and 20 pants.

• 15 shirts and 10 pants

• 25 shirts and 5 pants

A local charity is organizing a fundraiser. They plan to sell cookies and brownies. Each cookie costs $2, and each brownie costs $3. If they want to raise at least $200, write a system of inequalities to represent the number of cookies and brownies they need to sell. What are the possible combinations?

• 2x + 3y <= 200, x >= 0, y >= 0

• 2x + 3y = 200, x >= 0, y >= 0

• The system of inequalities is: 2x + 3y >= 200, x >= 0, y >= 0. Possible combinations can be found by solving these inequalities.

• x + y >= 100, x >= 0, y >= 0

A pet shelter has a limit of 50 animals. They have dogs and cats. Each dog requires 3 units of space, and each cat requires 2 units. If the shelter has 120 units of space available, write a system of inequalities to represent the number of dogs and cats they can take in. What are the possible combinations?

• (5, 55)

• (15, 30)

• (40, 10)

• The possible combinations of dogs and cats (x, y) are: (0, 60), (10, 40), (20, 20), (30, 0) within the limits.

A tech company is developing two products: a smartphone and a tablet. Each smartphone requires 4 hours of programming, and each tablet requires 3 hours. The team has a maximum of 60 hours available for development. Write a system of inequalities to represent the development limits. How many of each product can they develop?

• The maximum number of smartphones is 15 and tablets is 0, or any combination that satisfies 4x + 3y ≤ 60.

• The maximum number of smartphones is 20 and tablets is 2.

• The maximum number of smartphones is 10 and tablets is 5.

• The maximum number of smartphones is 5 and tablets is 15.