Exploring Real-Life Inequalities & Graphing Solutions

A farmer has a rectangular field. The length of the field is 3 meters more than twice the width. If the width must be less than 10 meters, graph the inequality that represents the possible dimensions of the field.

• 0 < w < 10, l = 2w + 3

• 0 < w < 15, l = 2w + 1

• 0 < w < 10, l = w + 3

• 0 < w < 5, l = 2w + 5

A school is planning to build a new playground. The area of the playground must be greater than 200 square meters but less than 400 square meters. Write and graph the inequalities that represent the area of the playground.

• 200 ≤ A ≤ 400

• 100 < A < 300

• 200 < A < 400

• A > 400

A store sells two types of fruit: apples and oranges. The store can sell a maximum of 50 fruits in a day. If the number of apples sold is represented by x and the number of oranges by y, write and graph the inequality that represents this situation.

• x + y = 50

• x + y < 50

• x + y ≤ 50

• x + y ≥ 50

A gym has a membership limit of 100 people. If the number of adult members is represented by x and the number of youth members by y, write the inequality that represents the maximum number of members and graph it.

• x + y ≥ 100

• x + y < 100

• x + y = 100

• x + y ≤ 100

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $50, write and graph the inequality that represents the maximum number of miles they can drive.

• m ≤ 120

• m ≤ 80

• m ≤ 90

• m ≤ 100

A local bakery sells cupcakes and cookies. The bakery can make a maximum of 80 items in a day. If the number of cupcakes is represented by x and the number of cookies by y, write and graph the inequality that represents this situation.

• x + y ≥ 80

• x + y < 80

• x + y = 80

• x + y ≤ 80

A concert venue has a seating capacity of 500. If the number of VIP seats is represented by x and general admission seats by y, write the inequality that represents the seating limit and graph it.

• x + y = 500

• x + y ≥ 500

• x + y ≤ 500

• x + y < 500

A charity event aims to raise at least $1,000. If each ticket sold is $20, write and graph the inequality that represents the minimum number of tickets that need to be sold.

• x = 40

• x ≤ 60

• x < 50

• x ≥ 50

A pizza shop offers two sizes of pizzas. The total number of pizzas sold in a day cannot exceed 60. If the number of large pizzas is represented by x and the number of small pizzas by y, write and graph the inequality that represents this situation.

• x + y ≤ 60

• x + y ≥ 60

• x + y < 60

• x + y = 60

A school is organizing a field trip and has a budget of $1,200. If each student pays $15, write and graph the inequality that represents the maximum number of students that can attend the trip.

• x ≤ 80

• x ≤ 75

• x ≤ 100

• x ≤ 60