Exploring Real-Life Inequalities: Graphing & Writing Skills

1. A school is planning a field trip and needs to rent buses. Each bus can hold 30 students. If the school has 150 students, write an inequality to represent the number of buses needed. Graph the inequality.

• b >= 5

• b = 6

• b <= 4

• b < 5

2. Maria is saving money to buy a new bike. She has $50 and saves $10 each week. Write an inequality to show how many weeks she needs to save to have at least $150. Graph the inequality.

• w <= 10

• w > 10

• w >= 10

• w < 10

3. A farmer has a total of 200 acres of land. He wants to plant corn and wheat. If he plants at least 50 acres of corn, write an inequality to represent the maximum acres of wheat he can plant. Graph the inequality.

• y ≤ 200

• y ≤ 150

• y ≤ 100

• y ≥ 50

4. A concert hall has a seating capacity of 500. If tickets are sold for $20 each, write an inequality to represent the maximum revenue if all tickets are sold. Graph the inequality.

• R ≤ 10000

• R = 10000

• R < 10000

• R ≥ 10000

5. A gym charges a monthly fee of $30 plus $5 for each class attended. Write an inequality to represent the total cost for attending 'x' classes in a month. Graph the inequality.

• 30 + 5x <= C

• C < 30 + 5x

• C >= 30 + 5x

• 30 + 5x = C

6. A bookstore sells novels for $15 each and textbooks for $25 each. If a student has $100 to spend, write an inequality to represent the maximum number of novels and textbooks they can buy. Graph the inequality.

• 10x + 20y ≤ 100

• 20x + 15y ≤ 100

• 5x + 30y ≤ 100

• 15x + 25y ≤ 100

7. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an inequality to represent the total cost for driving 'm' miles if the total cost must be less than $100. Graph the inequality.

• m < 250

• m < 200

• m < 300

• m < 150

8. A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer wants to spend no more than $50, write an inequality to represent the number of small and large pizzas they can buy. Graph the inequality.

• 2x + 3y ≤ 12

• 4x + y ≤ 15

• x + y ≤ 8

• 3x + 2y ≤ 10

9. A charity event aims to raise at least $2000. If each ticket sold is $25, write an inequality to represent the minimum number of tickets that need to be sold. Graph the inequality.

• x ≥ 80

• x < 80

• x ≤ 80

• x > 80

10. A student is planning to buy notebooks for $3 each and pens for $2 each. If they have $30 to spend, write an inequality to represent the maximum number of notebooks and pens they can buy. Graph the inequality.

• x + 5y ≤ 30

• 4x + y ≤ 30

• 3x + 2y ≤ 30

• 2x + 3y ≤ 30