Many inequality problems involve a starting fee plus a cost per item or hour.
The total cost must stay within a budget.
The inequality symbol shows the maximum amount allowed.
Use subtraction to remove the fixed cost first.
Divide to find the maximum number of items or hours.
✏️ Worked Examples — Writing and Solving Budget Inequalities
Example 1 — Bike Rental
Situation: A student has a budget of 💲120 to rent a bike. There is a one-time fee of 💲20, and the bike costs 💲10 per hour. How many hours can the student rent the bike and stay within the budget?
Define the variable: Let \(h\) represent the number of rental hours.
Interpretation: The student can rent the bike for 10 hours or fewer.
Example 2 — Party Room Rental
Situation: A family has a budget of 💲200 to rent a party room. There is a cleaning fee of 💲50, and the room costs 💲25 per hour. How many hours can they rent the room and stay within the budget?
Define the variable: Let \(h\) represent the number of rental hours.
Interpretation: The family can rent the room for 6 hours or fewer.
Example 3 — Game Rental
Situation: A gamer has a budget of 💲90 to rent video games. There is a membership fee of 💲15, and each game rental costs 💲8. How many games can the gamer rent and stay within the budget?
Define the variable: Let \(g\) represent the number of games rented.
Interpretation: Since the number of games must be a whole number, the gamer can rent 9 games or fewer.
🧠 Math Vocabulary
Budget: the maximum amount that can be spent.
Fixed Cost: a one-time fee that does not change.
Rate: the cost per item or per hour.
Inequality: a mathematical statement showing a comparison.
Solution: the values that make the inequality true.
💡 Main Idea
Many real-world situations involve a fixed fee plus a cost that depends on how much something is used. Writing and solving an inequality determines the maximum number of items or hours that stay within a budget.
📚 What You Should Already Know
Students should already know how to translate words into algebraic expressions and solve one-step equations using inverse operations.
🚀 What Comes Next
After learning how to write inequalities from real-world situations, students will solve and graph inequalities on a number line. They will also apply inequalities to multi-step situations, variables on both sides, and systems of inequalities.
🧩 Embed This Video in Your LMS
Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.
Copy and paste this code into your LMS to embed the video.
