Solving Real-Life Linear Inequalities: Graph & Interpret

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, how many acres of each crop can he plant?

• 30 acres of corn and 70 acres of wheat

• 20 acres of corn and 80 acres of wheat

• 50 acres of corn and 50 acres of wheat

• 10 acres of corn and 90 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 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 ≤ 25

• x ≥ 0 and x ≤ 20

• x ≥ 0 and x ≤ 10

• x ≥ 0 and x ≤ 14

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor and each Type B gadget requires 2 hours. The company has 60 hours of labor available. If they want to produce at least 10 gadgets in total, set up a system of inequalities and interpret the solution.

• The system of inequalities is: 3x + 2y ≤ 60 and x + y ≥ 10.

• x + 2y ≤ 60 and x + y ≥ 5

• 3x + 2y ≥ 60 and x + y ≤ 10

• 2x + 3y ≤ 60 and x + y ≥ 15

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, write a system of inequalities to represent the number of each type of membership sold.

• 30x + 50y = 1200, x >= 0, y >= 0

• 30x + 50y <= 1200, x >= 0, y >= 0

• 20x + 40y >= 1200, x >= 0, y >= 0

• 30x + 50y >= 1200, x >= 0, y >= 0

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, how many cakes of each type can they make if they want to make at least 5 cakes in total?

• 7 chocolate cakes and 5 vanilla cakes, or 0 chocolate cakes and 10 vanilla cakes.

• 10 chocolate cakes and 0 vanilla cakes

• 3 chocolate cakes and 8 vanilla cakes

• 5 chocolate cakes and 10 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 concert hall wants to make at least $15,000 from ticket sales, write a system of inequalities to represent the situation and graph it.

• x + y ≤ 500, 50x + 30y ≥ 15000

• x + y ≤ 400, 50x + 30y ≥ 20000

• x + y ≥ 500, 50x + 30y ≤ 15000

• x + y = 500, 50x + 30y = 15000

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. If the store wants to make at least $1,000 in sales and has a maximum of 50 items to sell, create a system of inequalities and interpret the solution.

• 20x + 30y = 1000 and x + y = 50

• The system of inequalities is: 20x + 30y >= 1000 and x + y <= 50.

• 20x + 30y <= 1000 and x + y >= 50

• 20x + 30y >= 500 and x + y <= 30

A charity event is selling tickets for a dinner. Each ticket costs $25, and they want to raise at least $2,000. If they can sell a maximum of 100 tickets, write a system of inequalities to represent the situation and graph it.

• 0 <= x <= 100

• 80 <= x <= 120

• 80 <= x <= 100

• 50 <= x <= 80

A tech company is developing two products: a smartphone and a tablet. Each smartphone requires 4 hours of development and each tablet requires 3 hours. If the company has 48 hours available and wants to develop at least 8 products in total, set up a system of inequalities and interpret the solution.

• The system of inequalities is: 4x + 3y ≤ 48 and x + y ≥ 8.

• 2x + 5y ≤ 48 and x + y ≥ 10

• 4x + 3y ≥ 48 and x + y ≤ 8

• x + 2y ≤ 48 and x + y ≤ 5

A local farmer's market sells fruits and vegetables. Each fruit basket costs $15 and each vegetable basket costs $10. If the market wants to earn at least $1,500 and can sell a maximum of 200 baskets, create a system of inequalities and graph it.

• x + y >= 200

• x >= 10, y >= 5

• 15x + 10y <= 1500

• 15x + 10y >= 1500, x + y <= 200, x >= 0, y >= 0