Exploring Real-Life Inequalities and Graphical Solutions

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 each crop can he plant?

• 70 acres of corn and 30 acres of wheat

• 80 acres of corn and 20 acres of wheat

• 50 acres of corn and 50 acres of wheat

• 60 acres of corn and 40 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 the inequality that represents the maximum number of students that can attend the trip.

• 35x <= 500

• 35x < 500

• 15x + 20x <= 500

• 20x <= 500

A gym offers two types of memberships: a monthly membership for $30 and an annual membership for $300. If a person can spend no more than $600 on memberships, how many monthly and annual memberships can they purchase?

• (15 monthly, 3 annual)

• (5 monthly, 5 annual)

• Possible combinations: (0 monthly, 2 annual), (10 monthly, 1 annual), (20 monthly, 0 annual)

• (1 monthly, 10 annual)

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 can bake for a total of 10 hours, how many cakes of each type can be made?

• 5 chocolate cakes and 5 vanilla cakes

• 0 chocolate cakes and 10 vanilla cakes

• 10 chocolate cakes and 0 vanilla cakes

• 2 chocolate cakes and 8 vanilla 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 total revenue from ticket sales cannot exceed $20,000, how many tickets of each type can be sold?

• 400 front row tickets and 100 back row tickets

• 250 front row tickets and 250 back row tickets

• 300 front row tickets and 200 back row tickets

• 500 back row tickets and 0 front row tickets

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

• 2x + 4y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 40, x ≥ 0, y ≥ 0

A charity event aims to raise at least $1,000. Each ticket sold contributes $25, and each donation contributes $50. Write an inequality to represent the relationship between the number of tickets sold (x) and donations (y) needed to meet the goal.

• 25x + 50y <= 1000

• 25x + 50y = 1000

• 25x + 50y >= 1000

• 25x + 50y > 1000

A restaurant has a maximum capacity of 200 customers. Each table for four seats 4 customers, and each table for two seats 2 customers. If the restaurant wants to maximize the number of customers seated, write a system of inequalities to represent the number of tables of each type that can be used.

• 3x + 2y ≤ 150, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 200, x ≥ 0, y ≥ 0

• 5x + 2y ≤ 250, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 200, x ≥ 0, y ≥ 0

A clothing store sells shirts for $15 and pants for $25. If the store wants to make at least $1,200 in sales, write an inequality that represents the minimum number of shirts (x) and pants (y) that need to be sold.

• 15x + 25y ≤ 1200

• 15x + 25y ≥ 1200

• 10x + 20y ≥ 1200

• 20x + 30y = 1200

A local park has a limit of 300 visitors at any given time. If each family of four counts as one visitor and each individual counts as one visitor, write an inequality to represent the number of families (x) and individuals (y) that can be in the park without exceeding the limit.

• x + 4y ≤ 300

• x + y ≤ 300

• 4x + y ≤ 300

• x + y < 300