A Cell Phone Provider Charges Felicia $\$ 50$ Per Month For Her Plan Plus $\$ 0.05$ Per Minute Of Long-distance Calls.If Felicia Wants To Keep Her Bill Under $\$ 55$, Which Inequality Should She Solve To

Feb 27, 2025 by ADMIN 213 views

A Cell Phone Provider's Charges: Understanding the Inequality

In today's digital age, cell phone plans have become an essential part of our daily lives. With various providers offering different plans and rates, it's crucial to understand how to calculate the total cost of our phone bills. In this article, we'll delve into the world of cell phone charges and explore the inequality that Felicia should solve to keep her bill under a certain amount.

Felicia is a cell phone user who wants to keep her monthly bill under $55. Her provider charges her $50 per month for her plan, plus $0.05 per minute of long-distance calls. To determine the maximum number of minutes she can talk without exceeding her budget, we need to set up an inequality.

Let's denote the number of minutes Felicia talks as ${x}$ . The total cost of her bill can be represented as the sum of the monthly plan fee and the cost of long-distance calls. Since the provider charges $0.05 per minute, the cost of long-distance calls can be calculated as ${0.05x}$ . The total cost of her bill is therefore:

${ \text{Total Cost} = 50 + 0.05x }$

Felicia wants to keep her bill under $55, so we can set up the following inequality:

${ 50 + 0.05x < 55 }$

To solve the inequality, we need to isolate the variable ${x}$ . Let's start by subtracting 50 from both sides of the inequality:

${ 0.05x < 55 - 50 }$

${ 0.05x < 5 }$

Next, we'll divide both sides of the inequality by 0.05 to solve for ${x}$ :

${ x < \frac{5}{0.05} }$

${ x < 100 }$

The inequality ${x < 100}$ tells us that Felicia can talk for a maximum of 100 minutes without exceeding her budget of $55. This means that if she talks for more than 100 minutes, her bill will exceed $55.

In conclusion, to keep her bill under $55, Felicia should solve the inequality ${x < 100}$ , where ${x}$ represents the number of minutes she talks. By understanding the inequality and its solution, Felicia can make informed decisions about her cell phone usage and stay within her budget.

The total cost of Felicia's bill is represented by the inequality ${50 + 0.05x < 55}$ .
To solve the inequality, we need to isolate the variable ${x}$ .
The solution to the inequality is ${x < 100}$ , which means Felicia can talk for a maximum of 100 minutes without exceeding her budget.

Understanding how to set up and solve inequalities like this one can have real-world applications in various fields, such as finance, economics, and data analysis. By being able to analyze and solve inequalities, individuals can make informed decisions about their finances and stay within their budgets.

In today's digital age, it's essential to understand how to calculate the total cost of our phone bills. By setting up and solving inequalities like the one in this article, individuals can make informed decisions about their cell phone usage and stay within their budgets. Whether you're a cell phone user or a math enthusiast, understanding inequalities can have a significant impact on your daily life.
A Cell Phone Provider's Charges: Understanding the Inequality - Q&A

In our previous article, we explored the world of cell phone charges and set up an inequality to determine the maximum number of minutes Felicia can talk without exceeding her budget. In this article, we'll answer some frequently asked questions related to the inequality and provide additional insights into the world of cell phone charges.

Q: What is the monthly plan fee?

A: The monthly plan fee is $50, which is the base cost of Felicia's cell phone plan.

Q: How much does it cost to make long-distance calls?

A: Felicia's provider charges $0.05 per minute for long-distance calls.

Q: What is the total cost of Felicia's bill?

A: The total cost of Felicia's bill is represented by the inequality $50 + 0.05x < 55$ , where $x$ is the number of minutes she talks.

Q: How do I solve the inequality?

A: To solve the inequality, we need to isolate the variable $x$ . We can do this by subtracting 50 from both sides of the inequality and then dividing both sides by 0.05.

Q: What is the solution to the inequality?

A: The solution to the inequality is $x < 100$ , which means Felicia can talk for a maximum of 100 minutes without exceeding her budget.

Q: What if I want to know the exact cost of my bill?

A: To find the exact cost of your bill, you can plug in the number of minutes you talk into the inequality $50 + 0.05x$ . For example, if you talk for 50 minutes, the total cost of your bill would be $50 + 0.05(50) = 50 + 2.50 = 52.50$ .

Q: Can I use this inequality to compare different cell phone plans?

A: Yes, you can use this inequality to compare different cell phone plans. By setting up an inequality for each plan, you can determine which plan is the most cost-effective for your needs.

Q: Are there any other factors I should consider when choosing a cell phone plan?

A: Yes, there are several other factors you should consider when choosing a cell phone plan, including:

Data limits: Some plans have data limits, which can affect your ability to stream videos or access the internet on your phone.
International coverage: If you travel frequently, you may want to choose a plan that offers international coverage.
Customer service: Consider the quality of customer service offered by each provider.
Additional features: Some plans may offer additional features, such as cloud storage or streaming services.

In conclusion, understanding how to set up and solve inequalities like the one in this article can have real-world applications in various fields, such as finance, economics, and data analysis. By being able to analyze and solve inequalities, individuals can make informed decisions about their finances and stay within their budgets.

The total cost of Felicia's bill is represented by the inequality $50 + 0.05x < 55$ .
To solve the inequality, we need to isolate the variable $x$ .
The solution to the inequality is $x < 100$ , which means Felicia can talk for a maximum of 100 minutes without exceeding her budget.
When choosing a cell phone plan, consider factors such as data limits, international coverage, customer service, and additional features.

Understanding how to set up and solve inequalities like the one in this article can have real-world applications in various fields, such as finance, economics, and data analysis. By being able to analyze and solve inequalities, individuals can make informed decisions about their finances and stay within their budgets.