Solving & Graphing Inequalities: Real-Life Budgeting Scenarios

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 the solution.

• Sarah can buy combinations of notebooks and pens such that 3x + 2y < 50, where x is the number of notebooks and y is the number of pens.

• Sarah can buy 10 notebooks and 5 pens for exactly $50.

• Sarah can only buy 15 pens and no notebooks.

• The inequality is 3x + 2y = 50.

2. A gym charges a $30 membership fee plus $10 per class. If you want to spend no more than $100, how many classes can you attend? Write and solve the inequality, then graph the solution.

• 3

• 7

• 10

• 5

3. A concert ticket costs $25, and you want to buy tickets for your friends without spending more than $200. If you also want to buy snacks for $5 each, how many tickets can you buy? Set up the inequality, solve it, and graph the solution.

• 10

• 6

• 12

• 8

4. A farmer has 120 acres of land. He wants to plant corn and soybeans, where corn requires 2 acres per unit and soybeans require 3 acres per unit. If he wants to plant less than 40 units total, write and solve the inequality, then graph the solution.

• The inequality to solve is 2x + 3y = 120 and x + y = 40.

• The solution set is the region where 2x + 3y ≤ 120 and x + y < 40, which can be graphed to show the feasible combinations of corn and soybeans.

• The farmer can plant a maximum of 60 units of corn and soybeans combined.

• The solution set is 2x + 3y ≥ 120 and x + y > 40.

5. A bookstore sells novels for $15 each and magazines for $5 each. If you want to spend less than $100, how many novels and magazines can you buy? Create the inequality, solve it, and graph the solution.

• You can buy up to 8 novels and 2 magazines.

• You can buy 4 novels and 20 magazines.

• You can buy up to 6 novels and 0 magazines, or combinations like (0, 19), (1, 17), (2, 15), (3, 13), (4, 11), (5, 9), (6, 0) while spending less than $100.

• You can buy 10 novels and 5 magazines.

6. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you want to spend no more than $100, how many miles can you drive? Write the inequality, solve it, and graph the solution.

• 150 miles

• 200 miles

• 250 miles

• 300 miles

7. A school is planning a field trip and has a budget of $300. If each student ticket costs $15 and each adult ticket costs $20, how many tickets can they buy if they want to stay under budget? Set up the inequality, solve it, and graph the solution.

• 15 tickets total

• The maximum number of tickets they can buy while staying under budget is 20 tickets (combination of student and adult tickets).

• 25 tickets total

• 10 adult tickets only

8. A pizza shop sells large pizzas for $12 each and drinks for $2 each. If you want to spend less than $50 for a party, how many pizzas and drinks can you buy? Write the inequality, solve it, and graph the solution.

• You can buy up to 5 pizzas and 0 drinks.

• You can buy up to 4 pizzas and 1 drink, or combinations like (0, 24), (1, 19), (2, 13), (3, 7), (4, 1).

• You can buy up to 3 pizzas and 10 drinks.

• You can buy up to 2 pizzas and 20 drinks.

9. A clothing store has a sale where jeans cost $30 each and shirts cost $20 each. If you want to spend less than $150, how many jeans and shirts can you buy? Create the inequality, solve it, and graph the solution.

• You can buy a maximum of 10 jeans and 5 shirts.

• You can buy a maximum of 2 jeans and 8 shirts.

• You can buy a maximum of 7 jeans and 1 shirt.

• You can buy a maximum of 5 jeans and 0 shirts, or combinations like 4 jeans and 3 shirts, or 3 jeans and 6 shirts, etc., as long as 3x + 2y < 15.

10. A student has $80 to spend on books and supplies. If textbooks cost $25 each and supplies cost $10 each, how many of each can the student buy without exceeding the budget? Write the inequality, solve it, and graph the solution.

• 1 textbook and 7 supplies

• 0 textbooks and 8 supplies

• The student can buy a maximum of 3 textbooks and 0 supplies, or combinations like 2 textbooks and 3 supplies, etc.

• 4 textbooks and 0 supplies