Problem 16
Question
For the following exercises, use this scenario: A wiress carrier offers the following plans that a person is considering. The Family Plan: s90 monthly fee, unlimited talk and text on up to 5 lines, and data charges of \(\$ 40\) for each device for up to 2 \(\mathrm{GB}\) of data per device. The Mobile Share Plan: \(\$ 120\) monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of \(\$ 35\) for each device up to a shared total of 10 \(\mathrm{GB}\) of data. Use \(P\) for the number of devices that need data plans as part of their cost. If a family has 3 smart phones, which plan should they choose?
Step-by-Step Solution
Verified Answer
The Family Plan is the cheaper option at $210 per month.
1Step 1: Understand the Family Plan Costs
The Family Plan includes a \(90 monthly fee. For each device, there's a \)40 charge for up to 2 GB of data. With 3 smartphones, the data cost would be \(40 \( \times \) 3 = \)120. The total cost for the Family Plan is \(90 + \)120 = $210.
2Step 2: Understand the Mobile Share Plan Costs
The Mobile Share Plan has a \(120 monthly fee. Each device is charged \)35 for data, up to a shared 10 GB. For 3 devices, the data cost would be \(35 \( \times \) 3 = \)105. The total cost for the Mobile Share Plan is \(120 + \)105 = $225.
3Step 3: Compare the Two Plans
For the Family Plan, the total monthly cost is $210, while the Mobile Share Plan costs $225. Therefore, the Family Plan is cheaper by $15.
Key Concepts
Wireless PlansData ChargesMonthly FeeSmartphones
Wireless Plans
When searching for the best wireless plan, individuals are often presented with several options tailored to different needs. Each plan typically comes with unique features and pricing structures. In our scenario, there are two wireless plans up for consideration: the Family Plan and the Mobile Share Plan.
The **Family Plan** offers a balanced proposition for smaller groups or families who rely minimally on multiple devices. It provides unlimited talk and text on up to 5 lines, ensuring communication is constant and without worry.
On the other hand, the **Mobile Share Plan** is designed for larger families or groups with multiple devices, supporting up to 10 lines. This plan is ideal for those who share data across many users, providing flexibility for larger shares of usage. Understanding the specific features and limitations of such plans is critical for making an informed decision.
The **Family Plan** offers a balanced proposition for smaller groups or families who rely minimally on multiple devices. It provides unlimited talk and text on up to 5 lines, ensuring communication is constant and without worry.
On the other hand, the **Mobile Share Plan** is designed for larger families or groups with multiple devices, supporting up to 10 lines. This plan is ideal for those who share data across many users, providing flexibility for larger shares of usage. Understanding the specific features and limitations of such plans is critical for making an informed decision.
Data Charges
Data charges are a pivotal factor in determining the overall cost of a wireless plan. In these scenarios, each plan has a distinct approach to how data usage is billed.
In the **Family Plan**, the data charges are distinct for each device. Each device incurs a cost of $40 for up to 2 GB of data. For families with multiple devices, this can add up quickly if not monitored closely.
The **Mobile Share Plan** introduces the concept of shared data, where several devices consume data from a common pool. Here, the charge is $35 per device, but the total data is capped at a shared 10 GB. This setup might be beneficial for families who wish to balance data use among devices efficiently.
Understanding these data charge structures helps users anticipate their monthly expenses based on device usage habits.
In the **Family Plan**, the data charges are distinct for each device. Each device incurs a cost of $40 for up to 2 GB of data. For families with multiple devices, this can add up quickly if not monitored closely.
The **Mobile Share Plan** introduces the concept of shared data, where several devices consume data from a common pool. Here, the charge is $35 per device, but the total data is capped at a shared 10 GB. This setup might be beneficial for families who wish to balance data use among devices efficiently.
Understanding these data charge structures helps users anticipate their monthly expenses based on device usage habits.
Monthly Fee
The monthly fee in a wireless plan is the recurring cost associated with maintaining the basic services of the plan. For any user, evaluating the monthly fee in context with other charges is crucial for full cost assessment.
The **Family Plan** requires a $90 monthly fee. This **base fee** ensures unlimited talk and text across up to five lines, a major component of the plan's value proposition.
Conversely, the **Mobile Share Plan** demands a higher base cost of $120 monthly. While this might seem steep initially, it caters to more devices and offers large-scale data sharing capacities.
Reviewing these fees in addition to per-device costs makes it easier for users to select the plan that aligns best with their usage and budgetary constraints.
The **Family Plan** requires a $90 monthly fee. This **base fee** ensures unlimited talk and text across up to five lines, a major component of the plan's value proposition.
Conversely, the **Mobile Share Plan** demands a higher base cost of $120 monthly. While this might seem steep initially, it caters to more devices and offers large-scale data sharing capacities.
Reviewing these fees in addition to per-device costs makes it easier for users to select the plan that aligns best with their usage and budgetary constraints.
Smartphones
Smartphones are integral in our daily lives and play a significant role in choosing the right wireless plan. They are the primary means through which users access talk, text, and data services.
In the scenario of a family with 3 smartphones, evaluating the cost efficiency of both plans becomes crucial. Here, each phone represents an individual data consumption source, affecting overall costs significantly.
For the **Family Plan**, 3 smartphones would incur a manageable cost due to the fixed monthly fee and individual data charges, making this plan more competitive for a small set of smartphones.
The **Mobile Share Plan** benefits larger setups by distributing the data cap among several devices, though it is slightly more expensive with a higher base fee.
Thus, the specific smartphone usage patterns within the family unit dictate the most cost-effective choice between different service options.
In the scenario of a family with 3 smartphones, evaluating the cost efficiency of both plans becomes crucial. Here, each phone represents an individual data consumption source, affecting overall costs significantly.
For the **Family Plan**, 3 smartphones would incur a manageable cost due to the fixed monthly fee and individual data charges, making this plan more competitive for a small set of smartphones.
The **Mobile Share Plan** benefits larger setups by distributing the data cap among several devices, though it is slightly more expensive with a higher base fee.
Thus, the specific smartphone usage patterns within the family unit dictate the most cost-effective choice between different service options.
Other exercises in this chapter
Problem 16
For the following exercises, solve each rational equation for \(x\). State all \(x\) -values that are excluded from the solution set. $$ \frac{3}{x}-\frac{1}{3}
View solution Problem 16
Solve the quadratic equation by factoring. $$ 4 x^{2}=5 x $$
View solution Problem 16
For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$5 x+2 y=0$$
View solution Problem 16
Solve each rational equation for x. State all x-values that are excluded from the solution set. \(\frac{3}{x}-\frac{1}{3}=\frac{1}{6}\)
View solution