Mastering Algebra: Inequalities & Boundary Points Challenge

1. Sarah has at least $50 to spend on books. If each book costs $12, how many books can she buy? Write the inequality and identify the boundary point.

• 5

• 6

• 3

• 4

2. A school is planning a field trip and needs to collect at least $300. If each student contributes $15, how many students need to participate? Set up the inequality and find the boundary point.

• 15

• 20

• 30

• 25

3. Tom is saving money for a video game that costs $60. If he saves $5 each week, write an inequality to represent how many weeks it will take him to save enough money. Identify the boundary point.

• 5w > 60; boundary point: w = 13

• 5w <= 60; boundary point: w = 10

• 5w >= 60; boundary point: w = 12

• 5w < 60; boundary point: w = 11

4. A gym charges a monthly fee of $30 plus $5 for each class attended. If you want to spend no more than $100 in a month, write an inequality and find the maximum number of classes you can attend.

• 16

• 12

• 14

• 10

5. Lisa wants to buy a new phone that costs $400. If she saves $50 each month, write an inequality to show how many months it will take her to save enough money. Identify the boundary point.

• m < 8, boundary point is 6 months

• m <= 8, boundary point is 9 months

• m >= 8, boundary point is 8 months

• m > 8, boundary point is 7 months

6. A farmer has a budget of $200 to buy seeds. If each packet of seeds costs $8, write an inequality to determine how many packets he can buy. Identify the boundary point.

• 8x <= 200; boundary point is x = 25

• 8x >= 200; boundary point is x = 30

• 8x + 50 <= 200; boundary point is x = 18

• 8x < 200; boundary point is x = 20

7. A concert hall has a seating capacity of 500. If each ticket costs $20, write an inequality to represent the total revenue if all tickets are sold. Identify the boundary point for maximum revenue.

• R <= 10000, boundary point is 10000

• R < 10000, boundary point is 5000

• R = 10000, boundary point is 15000

• R >= 10000, boundary point is 20000

8. A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If you want to spend no more than $100, write an inequality and find the maximum number of miles you can drive.

• 200

• 300

• 240

• 150

9. A student needs to score at least 75% on a test to pass. If the test has 40 questions, write an inequality to find the minimum number of questions he must answer correctly. Identify the boundary point.

• 30

• 25

• 40

• 35

10. A store is having a sale where you can buy 3 shirts for $45. If you want to spend no more than $90, write an inequality to find out how many shirts you can buy. Identify the boundary point.

• x <= 7, boundary point is 7

• x <= 6, boundary point is 6

• x <= 5, boundary point is 5

• x < 6, boundary point is 5