Problem 50 - Prealgebra

Question

After the included minutes have been exhausted, a cell phone company charges an additional \(\$ 0.08\) per minute. Plan A uses a flat rate of \(\$ 0.10\) per minute. Which plan is the least costly if a person uses 750 minutes per month? $$\begin{array}{|c|c|c|} \hline \text { Plan } & \begin{array}{c} \text { Monthly } \\ \text { Fee } \end{array} & \begin{array}{c} \text { Induded } \\ \text { Minutes } \end{array} \\ \hline \mathrm{A} & \$ 0 & \text { None } \\ \hline \mathrm{B} & \$ 29.99 & 500 \\ \hline \mathrm{C} & \$ 39.99 & 1,000 \\ \hline \mathrm{D} & \$ 49.99 & 1,500 \\ \hline \end{array}$$ A Plan A C Plan C B Plan B D Plan D

Step-by-Step Solution

Answer

Plan C is the least costly at \$39.99.

Step 1: Calculate Cost for Plan A

Plan A charges a flat rate of \( \\(0.10 \) per minute. For 750 minutes, calculate the total cost: \( 750 \times 0.10 = \\)75.00 \).

Step 2: Calculate Cost for Plan B

Plan B includes 500 minutes in the monthly fee of \\(29.99. For the extra 250 minutes beyond the included 500, the cost is \( 250 \times 0.08 = \\)20.00 \). Add this to the monthly fee: \( 29.99 + 20.00 = \$49.99 \).

Step 3: Calculate Cost for Plan C

Plan C includes 1,000 minutes for a monthly fee of \\(39.99. Since 750 minutes is within the included 1,000, no extra charge is needed. Thus, the total cost is \\)39.99.

Step 4: Calculate Cost for Plan D

Plan D includes 1,500 minutes for a monthly fee of \\(49.99. Since 750 minutes is within the included 1,500, no extra charge is needed. Thus, the total cost is \\)49.99.

Step 5: Compare Costs

Compare the total costs for each plan: \(\\(75.00\) for Plan A, \(\\)49.99\) for Plan B, \(\\(39.99\) for Plan C, \(\\)49.99\) for Plan D. Plan C has the lowest cost at \$39.99.

Key Concepts

Understanding Cell Phone Plans

Selecting the right cell phone plan can save you money and meet your communication needs. Cell phone plans vary mainly by:

• Monthly fees: Some plans charge a fixed monthly fee while others have no such obligation.
• Included minutes: Plans come with a certain number of call minutes included in the monthly fee.
• Additional charges: Any usage beyond the included minutes often incurs extra per-minute charges.

These factors can significantly affect the monthly cost depending on your usage. For instance, if you frequently exceed the included minutes, a plan with a lower per-minute overage fee might be more cost-effective.
This all means, finding the plan that best suits your needs involves evaluating how you use your phone each month.

Calculation of Plan Costs

Once you understand the details of cell phone plans, it's important to know how to calculate the total monthly cost effectively. Here's how you can do it:

• Determine your monthly usage: Know approximately how many minutes you'll use.
• Calculate the cost: For each plan, multiply the cost per additional minute by the number of minutes above the included amount.
• Add the base fee: Combine the calculated overage cost with any fixed monthly fee.

For example, Plan A charges a flat rate of \( \\(0.10 \) per minute, leading to a total monthly charge of \( 750 \times \\)0.10 = \\(75.00 \) for 750 minutes. Meanwhile, Plan B includes 500 minutes in the monthly fee of \( \\)29.99 \), and the additional 250 minutes result in \( 250 \times \\(0.08 = \\)20.00 \), making the total \( \$49.99 \). By following similar steps, you can determine costs for other plans, making it easier to compare them.

Conducting Choice Analysis

After calculating costs for each plan, the next step is choice analysis to decide which plan best meets your needs. Some key points to consider include:

• Lowest total cost: Determine which plan has the lowest overall cost for your usage level.
• Suitability: Consider which plan offers the most appropriate balance of cost, included minutes, and additional fees.
• Future needs: Think about how your usage might change, and choose a plan that can accommodate that growth without excessive cost.

In this instance, Plan C stands out because it offers enough minutes without additional charges at a cost of \( \$39.99 \), making it the most economical choice for 750 minutes of usage. This decision-making process involves weighing all elements to ensure maximum value and effectiveness.