Inequalities in Action: Solve and Graph Multi-Step Challenges

1. Sarah has $50 to spend on books. Each book costs $8. If she wants to buy at least 3 books, what is the maximum number of books she can buy? Solve the inequality and graph it on a number line.

• 6

• 7

• 5

• 4

2. A school is planning a field trip and needs to raise at least $300. If each student contributes $15, how many students need to participate to meet the goal? Write and solve the inequality, then graph it.

• 20

• 25

• 15

• 30

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, how many classes can they attend? Set up the inequality, solve it, and graph the solution.

• 16

• 14

• 10

• 12

4. A car rental company charges a flat fee of $20 plus $0.25 per mile driven. If a customer wants to keep their total cost under $50, how many miles can they drive? Create the inequality, solve it, and represent it on a number line.

• The customer can drive up to 75 miles.

• The customer can drive up to 100 miles.

• The customer can drive up to 119 miles.

• The customer can drive up to 150 miles.

5. Emily is saving money for a new bike that costs $150. She saves $10 each week. If she wants to buy the bike in less than 10 weeks, how much money does she need to have saved by then? Formulate the inequality, solve it, and graph the result.

• $150

• $200

• $120

• $100

6. A concert hall has a seating capacity of 500. If tickets are sold for $20 each, how many tickets must be sold to make at least $8,000? Write the inequality, solve it, and graph the solution on a number line.

• 450 tickets must be sold.

• 300 tickets must be sold.

• At least 400 tickets must be sold.

• 500 tickets must be sold.

7. A recipe requires at least 2 cups of flour and 1 cup of sugar. If each cup of flour costs $3 and each cup of sugar costs $2, how much can you spend if you want to make at least 5 batches of the recipe? Set up the inequality, solve it, and graph it.

• $30

• $40

• $50

• $25

8. A store is having a sale where you can buy 3 shirts for $45. If you want to spend no more than $90, how many shirts can you buy? Write the inequality, solve it, and represent it on a number line.

• 6 shirts

• 4 shirts

• 8 shirts

• 10 shirts

9. A gardener needs to plant at least 100 flowers. If each flower costs $2 and the gardener has $150, how many flowers can they plant? Create the inequality, solve it, and graph the solution.

• 100 flowers can be planted.

• 75 flowers can be planted.

• 50 flowers can be planted.

• 0 flowers can be planted.

10. A student has a budget of $60 for school supplies. If notebooks cost $5 each and pens cost $2 each, how many of each can they buy if they want at least 5 notebooks? Write the inequality, solve it, and graph the result on a number line.

• The student can buy 5 notebooks and 10 pens.

• The student can buy 8 notebooks and 5 pens.

• The student can buy 12 notebooks and 2 pens.

• The student can buy at least 5 notebooks and up to 17 pens.