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, Assuming

Introduction

As the cost of gasoline continues to rise, it's essential for individuals to manage their fuel expenses effectively. In this scenario, Nala is faced with a budget constraint of $\$150$ per month on gasoline. She has already spent $\$60$ on gas this month, leaving her with a limited amount for the remaining fill-ups. In this article, we will explore the mathematical inequality that can be used to determine the maximum number of fill-ups Nala can purchase during the rest of the month.

Understanding the Problem

Let's break down the problem step by step:

1. Nala's total budget for gasoline is $\$150$ per month.
2. She has already spent $\$60$ on gas this month.
3. We need to find the maximum number of fill-ups she can purchase during the rest of the month.

Setting Up the Inequality

To solve this problem, we can use a linear inequality. Let's denote the number of fill-ups Nala can purchase during the rest of the month as $x$. Since each fill-up costs a fixed amount, we can represent the total cost of fill-ups as $y$. We know that the total cost of fill-ups cannot exceed Nala's remaining budget, which is $\$150 - \$60 = \$90$. Therefore, we can set up the following inequality:

$$y \leq 90$$

However, we need to express $y$ in terms of $x$. Let's assume that each fill-up costs a fixed amount, say $\$c$. Then, the total cost of fill-ups can be represented as:

$$y = cx$$

Substituting this expression into the inequality, we get:

$$cx \leq 90$$

Solving the Inequality

To find the maximum number of fill-ups Nala can purchase, we need to solve the inequality for $x$. We can do this by dividing both sides of the inequality by $c$:

$$x \leq \frac{90}{c}$$

This inequality tells us that the maximum number of fill-ups Nala can purchase is $\frac{90}{c}$.

Interpreting the Results

The inequality $x \leq \frac{90}{c}$ provides us with a mathematical expression for the maximum number of fill-ups Nala can purchase. However, to determine the actual value of $x$, we need to know the cost of each fill-up, represented by $c$. Once we have this information, we can plug it into the inequality to find the maximum number of fill-ups.

Conclusion

In conclusion, the inequality $x \leq \frac{90}{c}$ can be used to find the maximum number of fill-ups Nala can purchase during the rest of the month. By substituting the cost of each fill-up into the inequality, we can determine the actual value of $x$. This mathematical approach provides a clear and concise solution to the problem, helping Nala manage her gasoline expenses effectively.

Example Use Case

Let's consider an example to illustrate the application of the inequality. Suppose the cost of each fill-up is $\$20$. We can plug this value into the inequality to find the maximum number of fill-ups Nala can purchase:

$$x \leq \frac{90}{20}$$

Simplifying the expression, we get:

$$x \leq 4.5$$

Since Nala cannot purchase a fraction of a fill-up, we can round down to the nearest whole number:

$$x \leq 4$$

Therefore, Nala can purchase a maximum of 4 fill-ups during the rest of the month.

Real-World Applications

The mathematical inequality $x \leq \frac{90}{c}$ has real-world applications in various fields, including:

• Personal finance: This inequality can be used to manage personal expenses, such as gasoline, food, or entertainment costs.
• Business planning: Companies can use this inequality to determine the maximum number of products they can produce or services they can offer within a given budget.
• Resource allocation: This inequality can be applied to allocate resources, such as personnel, equipment, or materials, within a limited budget.

Limitations and Future Work

While the inequality $x \leq \frac{90}{c}$ provides a useful solution to the problem, there are some limitations to consider:

• Assumptions: The inequality assumes that the cost of each fill-up is fixed and known. In reality, costs may vary depending on factors such as location, time of day, or weather conditions.
• Uncertainty: The inequality does not account for uncertainty or variability in the cost of fill-ups. In a real-world scenario, costs may fluctuate, affecting the maximum number of fill-ups Nala can purchase.

Future work could involve developing more sophisticated models that account for these limitations and provide a more accurate representation of the problem.

Conclusion

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Introduction

In our previous article, we explored the mathematical inequality $x \leq \frac{90}{c}$ that can be used to find the maximum number of fill-ups Nala can purchase during the rest of the month. In this article, we will address some common questions and concerns related to this inequality.

Q: What is the significance of the cost of each fill-up, represented by c?

A: The cost of each fill-up, represented by c, is a critical factor in determining the maximum number of fill-ups Nala can purchase. This cost can vary depending on factors such as location, time of day, or weather conditions. By knowing the cost of each fill-up, Nala can accurately calculate the maximum number of fill-ups she can purchase.

Q: How can I determine the cost of each fill-up, c?

A: The cost of each fill-up, c, can be determined by dividing the total cost of fill-ups by the number of fill-ups. For example, if the total cost of fill-ups is $90 and the number of fill-ups is 4, then the cost of each fill-up is $90 ÷ 4 = $22.50.

Q: What if the cost of each fill-up varies depending on the location or time of day?

A: In this case, the inequality $x \leq \frac{90}{c}$ may not provide an accurate representation of the problem. A more sophisticated model would be needed to account for the variability in the cost of fill-ups.

Q: Can I use this inequality to determine the maximum number of fill-ups for a specific time period, such as a week or a month?

A: Yes, the inequality $x \leq \frac{90}{c}$ can be used to determine the maximum number of fill-ups for a specific time period. Simply adjust the total cost of fill-ups to reflect the time period in question.

Q: What if I have a budget constraint that is not a fixed amount, but rather a percentage of my income?

A: In this case, the inequality $x \leq \frac{90}{c}$ may not provide an accurate representation of the problem. A more sophisticated model would be needed to account for the variable budget constraint.

Q: Can I use this inequality to determine the maximum number of fill-ups for a specific type of vehicle, such as a car or a truck?

A: Yes, the inequality $x \leq \frac{90}{c}$ can be used to determine the maximum number of fill-ups for a specific type of vehicle. Simply adjust the cost of each fill-up to reflect the fuel efficiency of the vehicle in question.

Q: What if I have multiple budget constraints, such as a budget for gasoline and a budget for other expenses?

A: In this case, the inequality $x \leq \frac{90}{c}$ may not provide an accurate representation of the problem. A more sophisticated model would be needed to account for the multiple budget constraints.

Conclusion

In conclusion, the inequality $x \leq \frac{90}{c}$ provides a mathematical solution to the problem of determining the maximum number of fill-ups Nala can purchase during the rest of the month. By addressing common questions and concerns related to this inequality, we can better understand its significance and limitations.

Real-World Applications

The mathematical inequality $x \leq \frac{90}{c}$ has real-world applications in various fields, including:

• Personal finance: This inequality can be used to manage personal expenses, such as gasoline, food, or entertainment costs.
• Business planning: Companies can use this inequality to determine the maximum number of products they can produce or services they can offer within a given budget.
• Resource allocation: This inequality can be applied to allocate resources, such as personnel, equipment, or materials, within a limited budget.

Limitations and Future Work

While the inequality $x \leq \frac{90}{c}$ provides a useful solution to the problem, there are some limitations to consider:

• Assumptions: The inequality assumes that the cost of each fill-up is fixed and known. In reality, costs may vary depending on factors such as location, time of day, or weather conditions.
• Uncertainty: The inequality does not account for uncertainty or variability in the cost of fill-ups. In a real-world scenario, costs may fluctuate, affecting the maximum number of fill-ups Nala can purchase.

Future work could involve developing more sophisticated models that account for these limitations and provide a more accurate representation of the problem.

Conclusion

In conclusion, the inequality $x \leq \frac{90}{c}$ provides a mathematical solution to the problem of determining the maximum number of fill-ups Nala can purchase during the rest of the month. By addressing common questions and concerns related to this inequality, we can better understand its significance and limitations.