Real-Life Linear Inequalities: Variables and Constraints

A local gym charges a monthly fee of $30 plus $5 for each class attended. Write a linear inequality to represent the total cost (C) for attending x classes in a month. What is the maximum number of classes you can attend if your budget is $100?

• 16

• 14

• 10

• 12

A farmer has 200 feet of fencing to create a rectangular pen for sheep. If the length of the pen is represented by x and the width by y, write a linear inequality to represent the area of the pen. What are the possible dimensions if the area must be less than 1000 square feet?

• Possible dimensions (x, y) are: x < 10 or x > 90, with y = 100 - x.

• x < 5 or x > 95, with y = 150 - x.

• x < 50 or x > 150, with y = 100 - x.

• x < 20 or x > 80, with y = 200 - x.

A school is planning a field trip and has a budget of $500. The cost per student is $15, and there is a fixed cost of $100 for the bus. Write a linear inequality to represent the number of students (s) that can attend. How many students can go if the school wants to spend no more than $500?

• 26

• 20

• 15

• 30

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and gadget B requires 3 hours. If the company has 24 hours of labor available, write a linear inequality to represent the production limits of gadgets A (a) and B (b). What combinations of gadgets can be produced?

• 2a + 3b = 24

• 4a + 2b ≤ 24

• 2a + 3b ≥ 24

• 2a + 3b ≤ 24

A concert hall has a seating capacity of 500. If tickets for the concert are sold at $20 each and the total revenue must be at least $8000, write a linear inequality to represent the number of tickets (t) that must be sold. What is the minimum number of tickets that need to be sold?

• 400

• 300

• 450

• 350

A bakery sells muffins for $2 each and cookies for $1 each. If the bakery wants to make at least $100 in sales, write a linear inequality to represent the number of muffins (m) and cookies (c) sold. How many of each can be sold to meet this goal?

• 2m + c >= 100

• m + 2c >= 100

• 3m + c <= 100

• m + c >= 50

A student is saving money for a new laptop that costs $800. If they save $50 each week and also have a one-time gift of $200, write a linear inequality to represent the number of weeks (w) needed to save enough money. How many weeks will it take to reach the goal?

• 10 weeks

• 15 weeks

• 20 weeks

• 12 weeks

A clothing store has a sale where jeans are $40 each and shirts are $25 each. If a customer wants to spend no more than $200, write a linear inequality to represent the number of jeans (j) and shirts (s) they can buy. What combinations of jeans and shirts can they purchase?

• 30j + 20s ≤ 200

• 50j + 15s ≤ 200

• 40j + 30s ≤ 200

• 40j + 25s ≤ 200

A charity event aims to raise at least $1500. If each ticket sold is $15 and there is a fixed cost of $300 for the venue, write a linear inequality to represent the number of tickets (t) that need to be sold. How many tickets must be sold to meet the fundraising goal?

• 100

• 120

• 130

• 150

A restaurant has a special where each burger costs $8 and each drink costs $2. If a family wants to spend no more than $50, write a linear inequality to represent the number of burgers (b) and drinks (d) they can order. What are the possible combinations of burgers and drinks they can choose?

• 8b + 2d ≤ 50; Possible combinations include (0, 25), (1, 21), (2, 17), (3, 13), (4, 9), (5, 5), (6, 1), etc.

• 10b + d ≤ 50

• 5b + 5d ≤ 50

• 7b + 3d ≤ 50