Nala Can Spend No More Than \[$\$150\$\] Per Month On Gasoline. She Has Already Purchased \[$\$60\$\] In Gas This Month. Which Inequality Can Be Used To Find The Maximum Number Of Fill-ups She Can Purchase During The Rest Of The Month,
Introduction
As the cost of living continues to rise, individuals are becoming increasingly mindful of their expenses. For Nala, a monthly budget of $150 for gasoline is a crucial consideration. With $60 already spent on gas this month, she must carefully plan her remaining expenses to ensure she stays within her allocated budget. In this article, we will explore the mathematical concept of inequalities and how it can be applied to determine the maximum number of gas fill-ups Nala can afford during the rest of the month.
Understanding Inequalities
In mathematics, an inequality is a statement that compares two values or expressions using a combination of greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) symbols. Inequalities are used to represent relationships between variables and are essential in solving problems involving constraints, such as budget limitations.
The Inequality Model
To find the maximum number of gas fill-ups Nala can purchase during the rest of the month, we need to establish an inequality model that takes into account her remaining budget and the cost of each fill-up. Let's assume the cost of each fill-up is $x. Since Nala has already spent $60, her remaining budget is $150 - $60 = $90.
The Inequality
The inequality that represents the situation can be written as:
90 ≥ 5x
Where 5x represents the total cost of gas fill-ups, and 90 is the remaining budget.
Solving the Inequality
To solve the inequality, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 5:
18 ≥ x
This means that the maximum cost of each gas fill-up is $18.
Interpreting the Results
Now that we have the inequality 18 ≥ x, we can use it to determine the maximum number of gas fill-ups Nala can purchase during the rest of the month. Since the cost of each fill-up is $18, we can divide the remaining budget ($90) by the cost of each fill-up ($18) to find the maximum number of fill-ups:
90 ÷ 18 = 5
Therefore, Nala can purchase a maximum of 5 gas fill-ups during the rest of the month.
Conclusion
In conclusion, the inequality 18 ≥ x provides a mathematical framework for determining the maximum number of gas fill-ups Nala can purchase during the rest of the month. By understanding the concept of inequalities and applying it to real-world problems, we can make informed decisions and stay within our allocated budgets.
Real-World Applications
The concept of inequalities has numerous real-world applications, including:
- Budgeting and financial planning
- Resource allocation and management
- Optimization problems in business and economics
- Decision-making in fields such as medicine, engineering, and science
Final Thoughts
In this article, we explored the mathematical concept of inequalities and its application to a real-world problem involving gas fill-ups. By using an inequality model, we were able to determine the maximum number of gas fill-ups Nala can purchase during the rest of the month. This example illustrates the importance of mathematical modeling in making informed decisions and staying within allocated budgets.
Additional Resources
For further reading on inequalities and mathematical modeling, we recommend the following resources:
- Khan Academy: Inequalities
- Math Is Fun: Inequalities
- Wolfram MathWorld: Inequalities
References
- [1] "Inequalities" by Khan Academy
- [2] "Inequalities" by Math Is Fun
- [3] "Inequalities" by Wolfram MathWorld
Frequently Asked Questions: Maximizing Gas Fill-Ups =====================================================
Introduction
In our previous article, we explored the mathematical concept of inequalities and its application to a real-world problem involving gas fill-ups. We established an inequality model to determine the maximum number of gas fill-ups Nala can purchase during the rest of the month. In this article, we will address some frequently asked questions related to maximizing gas fill-ups.
Q&A
Q: What is the maximum number of gas fill-ups Nala can purchase during the rest of the month?
A: According to the inequality 18 ≥ x, where x represents the cost of each gas fill-up, Nala can purchase a maximum of 5 gas fill-ups during the rest of the month.
Q: What is the remaining budget for Nala after purchasing $60 worth of gas this month?
A: Nala's remaining budget is $150 - $60 = $90.
Q: How did you determine the cost of each gas fill-up?
A: We assumed the cost of each gas fill-up is $x. Since Nala has already spent $60, her remaining budget is $150 - $60 = $90. We then divided the remaining budget by the number of fill-ups to determine the cost of each fill-up.
Q: Can Nala purchase more than 5 gas fill-ups during the rest of the month?
A: No, according to the inequality 18 ≥ x, the maximum cost of each gas fill-up is $18. Therefore, Nala can purchase a maximum of 5 gas fill-ups during the rest of the month.
Q: What if the cost of each gas fill-up is less than $18?
A: If the cost of each gas fill-up is less than $18, Nala can purchase more than 5 gas fill-ups during the rest of the month. For example, if the cost of each gas fill-up is $15, Nala can purchase 6 gas fill-ups during the rest of the month.
Q: How can I apply this concept to my own budgeting and financial planning?
A: You can apply this concept to your own budgeting and financial planning by identifying your remaining budget and the cost of each item or service you need to purchase. Then, use an inequality model to determine the maximum number of items or services you can purchase within your remaining budget.
Q: What are some real-world applications of inequalities in budgeting and financial planning?
A: Inequalities have numerous real-world applications in budgeting and financial planning, including:
- Budgeting and financial planning
- Resource allocation and management
- Optimization problems in business and economics
- Decision-making in fields such as medicine, engineering, and science
Conclusion
In conclusion, the concept of inequalities is a powerful tool for making informed decisions and staying within allocated budgets. By understanding how to apply inequalities to real-world problems, you can make more effective decisions and achieve your financial goals.
Additional Resources
For further reading on inequalities and mathematical modeling, we recommend the following resources:
- Khan Academy: Inequalities
- Math Is Fun: Inequalities
- Wolfram MathWorld: Inequalities
References
- [1] "Inequalities" by Khan Academy
- [2] "Inequalities" by Math Is Fun
- [3] "Inequalities" by Wolfram MathWorld