Solving and Graphing Linear Inequalities in Real-Life Scenarios

1. A school is planning a field trip and has a budget of $500. Each ticket costs $20. Write an inequality to represent the number of tickets (t) they can buy and graph it.

• t = 25

• t <= 25

• t < 20

• t >= 30

2. A farmer has 100 acres of land and wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour. If he has 120 hours of labor available, write and graph the inequality for the land usage.

• 2x + 2y <= 100, x + y >= 120

• x + y <= 100, 2x + y <= 120

• x + 2y <= 100, x + y <= 120

• x + y >= 100, 2x + y >= 120

3. A gym charges a monthly fee of $30 plus $5 for each class attended. If a member wants to spend no more than $100 in a month, write an inequality for the number of classes (c) they can attend and graph it.

• c ≤ 5

• c ≤ 10

• c ≤ 14

• c ≤ 20

4. A company produces x gadgets and y widgets. The production of gadgets requires 3 hours each, and widgets require 2 hours. If they have 60 hours available, write the inequality and graph the feasible region.

• 2x + 3y ≤ 60

• 3x + 2y ≤ 60

• 4x + y ≤ 60

• x + 2y ≤ 60

5. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality for the miles driven (m) and graph it.

• m ≤ 250

• m ≤ 300

• m ≤ 200

• m ≤ 150

6. A local bakery sells cupcakes for $2 each and cookies for $1 each. If they want to make at least $100 in a day, write an inequality for the number of cupcakes (c) and cookies (k) sold and graph it.

• 2c + k >= 100

• 2c + 3k >= 100

• 3c + k <= 100

• c + k >= 100

7. A student has a budget of $40 to spend on books. If each book costs $8, write an inequality to represent the number of books (b) they can buy and graph it.

• 8b <= 40, b <= 5

• 8b < 40, b < 5

• 8b = 40, b = 5

• 8b >= 40, b >= 5

8. A concert venue has a maximum capacity of 200 people. If tickets are sold for $15 each, write an inequality to represent the number of tickets (t) that can be sold and graph it.

• t <= 200

• t = 200

• t >= 200

• t < 200

9. A charity event aims to raise at least $1,000. If each ticket sold is $25, write an inequality for the number of tickets (t) that need to be sold and graph it.

• t <= 40

• t < 40

• t >= 40

• t > 40

10. A restaurant has a seating capacity of 150. If they want to maintain a minimum of 30 empty seats for safety, write an inequality for the number of customers (c) they can serve and graph it.

• c > 120

• c < 100

• c <= 120

• c >= 150