Graphing Linear Inequalities: Real-World Problems for 8th Grade

1. A local gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost (C) for attending x classes if you want to spend no more than $100. Graph the inequality and shade the solution region.

• C = 30 + 5x ≤ 80; x ≤ 14

• C = 30 + 5x = 100; x = 14

• C = 30 + 5x ≤ 100; x ≤ 14

• C = 30 + 5x ≥ 100; x ≥ 14

2. A farmer has 120 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 3 hours. If the farmer has a maximum of 240 hours available, write an inequality to represent the situation. Graph the inequality and shade the solution region.

• 2x + 3y ≥ 240, x + y ≤ 120

• x + 2y ≤ 240, x + y ≤ 100

• 2x + 3y ≤ 240, x + y ≤ 120

• 2x + 3y ≤ 200, x + y ≥ 120

3. A school is planning a field trip and can spend no more than $500. The cost per student is $15. Write an inequality to represent the number of students (s) that can attend the trip. Graph the inequality and shade the solution region.

• s >= 40

• s < 25

• s <= 33

• s = 30

4. A company produces two types of gadgets, A and B. Each gadget A requires 3 hours of labor, and each gadget B requires 2 hours. If the company has a maximum of 60 hours of labor available, write an inequality to represent the number of gadgets A (a) and B (b) that can be produced. Graph the inequality and shade the solution region.

• 4a + 3b ≤ 60

• 2a + 3b ≤ 60

• 3a + 2b ≤ 60

• 3a + 2b ≥ 60

5. A restaurant sells burgers for $8 and salads for $5. If the restaurant wants to make at least $200 in one day, write an inequality to represent the number of burgers (b) and salads (s) sold. Graph the inequality and shade the solution region.

• 5b + 8s ≥ 200

• 8b + 5s = 200

• 8b + 5s ≤ 200

• 8b + 5s ≥ 200

6. A student has a budget of $50 to spend on books. If each book costs $12, write an inequality to represent the number of books (b) the student can buy. Graph the inequality and shade the solution region.

• b < 5

• b = 4

• b <= 4

• b >= 5

7. A concert hall has a seating capacity of 300. If tickets for adults cost $20 and tickets for children cost $10, write an inequality to represent the number of adult (a) and child (c) tickets that can be sold if the total revenue must be at least $4000. Graph the inequality and shade the solution region.

• a + c ≤ 300 and 20a + 10c ≥ 4000

• a + c = 300 and 20a + 10c = 4000

• a + c < 300 and 20a + 10c < 4000

• a + c ≥ 300 and 20a + 10c ≤ 4000

8. A factory produces toys and games. Each toy requires 4 hours of production time, and each game requires 2 hours. If the factory has a maximum of 80 hours available, write an inequality to represent the number of toys (t) and games (g) that can be produced. Graph the inequality and shade the solution region.

• 4t + 2g ≥ 80

• 4t + 2g ≤ 80

• 3t + 5g ≤ 80

• 2t + 4g ≤ 80

9. A charity event aims to raise at least $1000. If each ticket sold is $25, write an inequality to represent the number of tickets (t) that need to be sold. Graph the inequality and shade the solution region.

• t ≥ 40

• t > 40

• t < 40

• t ≤ 40

10. A gardener has 50 feet of fencing to create a rectangular garden. If the length (l) must be greater than the width (w), write an inequality to represent the relationship between length and width. Graph the inequality and shade the solution region.

• l + w < 25 and l > w

• l + w < 50 and l = w

• l + w > 25 and l < w

• l + w = 50 and l < w