Exploring and Graphing Systems of Inequalities

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, write a system of inequalities to represent the situation and graph it.

• x + y <= 80, 2x + 3y <= 200

• x + y >= 100, 2x + 3y >= 240

• x + y <= 100, 2x + 3y <= 240

• x + y = 100, 2x + 3y = 240

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. Write a system of inequalities to determine the maximum number of students that can attend the trip, and graph the inequalities.

• x ≤ 5 and x ≥ 0, maximum number of students is 5.

• x ≤ 14 and x ≥ 0, maximum number of students is 14.

• x ≤ 10 and x ≥ 0, maximum number of students is 10.

• x ≤ 20 and x ≥ 0, maximum number of students is 20.

A store sells two types of bicycles: mountain bikes and road bikes. The store has a maximum of 50 bikes to sell and wants to sell at least 10 mountain bikes. Write a system of inequalities to represent the situation and solve for the number of each type of bike that can be sold.

• x <= 50 and y <= 10

• x >= 10 and y >= 0

• 10 <= x <= 50 and 0 <= y <= 50 - x

• x + y <= 50 and x >= 5

A local gym has a membership limit of 200 people. They currently have 120 members and want to add at least 30 new members. Write a system of inequalities to represent the situation and graph it.

• 120 + x <= 200, x >= 30

• 120 + x = 200, x > 30

• 120 + x >= 200, x < 30

• 120 + x < 200, x <= 30

A charity event aims to raise at least $1,000. They charge $10 per ticket and have a goal of selling at least 50 tickets. Write a system of inequalities to represent the situation and solve for the number of tickets that need to be sold.

• 200

• 150

• 100

• 75

A clothing store has a sale on shirts and pants. They want to sell at least 40 items in total, with at least 10 shirts. Write a system of inequalities to represent the situation and solve for the number of shirts and pants that can be sold.

• x >= 10, y <= 30 - x

• x >= 5, y >= 35 - x

• x <= 15, y >= 25 - x

• x >= 10, y >= 40 - x

A concert venue can hold a maximum of 500 people. They want to sell tickets for both general admission and VIP seating. Each VIP ticket costs $50, and each general admission ticket costs $20. Write a system of inequalities to represent the situation and graph it.

• x + y < 500, x > 0, y > 0

• x + y ≤ 600, x ≥ 0, y ≥ 0

• x + y = 500, x ≥ 0, y ≤ 0

• x + y ≤ 500, x ≥ 0, y ≥ 0

A bakery makes two types of cakes: chocolate and vanilla. They can make a maximum of 60 cakes in a day and want to make at least 20 chocolate cakes. Write a system of inequalities to represent the situation and solve for the number of each type of cake that can be made.

• The bakery can make between 20 to 60 chocolate cakes and between 0 to 40 vanilla cakes.

• The bakery can make 10 to 50 chocolate cakes and 10 to 30 vanilla cakes.

• The bakery can make 0 to 60 chocolate cakes and 0 to 60 vanilla cakes.

• The bakery can make 20 to 40 chocolate cakes and 20 to 20 vanilla cakes.

A community center has a budget of $1,200 for a summer camp. Each camper costs $150, and they want to have at least 5 campers. Write a system of inequalities to represent the situation and graph it.

• x >= 5 and x <= 8

• x >= 6 and x <= 9

• x >= 5 and x <= 12

• x >= 3 and x <= 10