Two-Step Inequalities: Graphing & Variables Challenge

1. Sarah has $50. She wants to buy some books that cost $12 each. Write a two-step inequality to represent how many books she can buy, and graph the solution on a number line.

• b < 4

• b <= 4

• b >= 4

• b <= 5

2. A school is planning a field trip and needs to collect at least $200. If each student contributes $15, write a two-step inequality to find out how many students need to contribute, and identify the variable and constants.

• At least 5 students

• At least 14 students

• At least 10 students

• At least 20 students

3. Tom is saving money to buy a new video game that costs $60. If he currently has $20 and saves $10 each week, write a two-step inequality to determine how many weeks it will take him to save enough money, and graph the solution.

• w <= 5

• w >= 4

• w = 3

• w < 4

4. A concert hall has a seating capacity of 300. If 120 tickets have already been sold, write a two-step inequality to find out how many more tickets can be sold, and identify the variable and constants.

• x + 120 ≤ 300

• x - 120 ≤ 300

• x + 120 < 300

• x + 120 = 300

5. Lisa is making bracelets to sell at a craft fair. Each bracelet costs her $5 to make. If she wants to make a profit of at least $50, write a two-step inequality to find out how many bracelets she needs to sell, and graph the solution on a number line.

• x <= 10

• x >= 5

• x >= 15

• x >= 10

6. A gym charges a monthly fee of $30. If you want to spend no more than $150 in 6 months, write a two-step inequality to represent this situation, and identify the variable and constants.

• 30x >= 150, where x is the number of months.

• 30x < 150, where x is the number of months.

• 30x <= 150, where x is the number of months.

• 30x + 150 <= 0, where x is the number of months.

7. A farmer has 120 apples and wants to pack them into boxes that hold 15 apples each. Write a two-step inequality to find out how many boxes he can fill, and graph the solution on a number line.

• The farmer can fill at most 5 boxes.

• The farmer can fill at most 10 boxes.

• The farmer can fill at most 12 boxes.

• The farmer can fill at most 8 boxes.

8. A movie theater has 200 seats. If 75 seats are already reserved, write a two-step inequality to find out how many more seats can be reserved, and identify the variable and constants.

• x ≤ 100

• x ≤ 125

• x < 75

• x ≥ 125

10. A student needs to score at least 70% on a test to pass. If the test has 50 questions, write a two-step inequality to find out how many questions the student needs to answer correctly, and identify the variable and constants.

• The student needs to answer at least 25 questions correctly.

• The student needs to answer at least 50 questions correctly.

• The student needs to answer at least 35 questions correctly.

• The student needs to answer at least 40 questions correctly.