Inequalities in Action: Graphing and Solving for Budgeting

1. Sarah has $50 to spend on school supplies. If she buys notebooks for $3 each and pens for $2 each, how many notebooks and pens can she buy if she wants to spend less than $50? Solve the inequality and graph it on a number line.

• Sarah can buy 0 to 16 notebooks and corresponding pens such that the total cost is less than $50.

• Sarah can buy 10 notebooks and 15 pens.

• Sarah can buy 20 notebooks and no pens.

• Sarah can buy 5 notebooks and 25 pens.

2. A concert hall has a seating capacity of 500. If tickets are sold for $20 each, how many tickets can be sold if the total revenue must be less than $10,000? Write and solve the inequality, then represent it on a number line.

• 499

• 600

• 450

• 500

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.

• 10

• 12

• 16

• 14

4. A farmer has a budget of $200 to buy seeds. If each packet of seeds costs $15 and he also needs to pay a $10 delivery fee, how many packets can he buy without exceeding his budget? Formulate the inequality, solve it, and illustrate it on a number line.

• 8

• 15

• 12

• 10

5. A student is saving money for a new laptop that costs $800. If they save $50 a week, how many weeks will it take to save enough money if they want to save at least $800? Create the inequality, solve it, and graph the result.

• 10 weeks

• 20 weeks

• 16 weeks

• 12 weeks

6. A bookstore is having a sale where each book costs $12. If a customer wants to buy books without spending more than $60, how many books can they purchase? Write the inequality, solve it, and represent it on a number line.

• 4

• 3

• 5

• 6

7. A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If a customer wants to keep their total cost under $100, how many miles can they drive? Set up the inequality, solve it, and graph the solution.

• 239 miles

• 200 miles

• 300 miles

• 150 miles

8. A school is planning a field trip and has a budget of $1,200. If each student ticket costs $15 and there is a $300 bus fee, how many students can attend without exceeding the budget? Formulate the inequality, solve it, and illustrate it on a number line.

• 80

• 70

• 60

• 50

9. A pet store sells fish for $5 each and aquariums for $30 each. If a customer wants to spend less than $100, how many fish and aquariums can they buy? Create the inequality, solve it, and graph the result.

• The customer can buy up to 19 fish and 0 aquariums, 13 fish and 1 aquarium, 7 fish and 2 aquariums, or 1 fish and 3 aquariums.

• 10 fish and 5 aquariums

• 20 fish and 0 aquariums

• 5 fish and 4 aquariums

10. A family is planning a vacation and has a budget of $2,000. If they plan to spend $150 per day on accommodations and $50 per day on food, how many days can they afford to stay? Write the inequality, solve it, and represent it on a number line.

• 8 days

• 15 days

• 5 days

• 10 days