Problem 26 - Prealgebra

Question

All cell phone plans are not created equal. The number of minutes and the monthly charges can vary greatly. The table shows four plans presented by four different cell phone providers. $$\begin{array}{|l|cccc|} \hline \text { Cames } & \text { Alciu } & \text { Sumple } & \text { UMGSTIO } & \text { VILERIN } \\ \hline \text { Plan name } & \begin{array}{c} \text { Nation } \\ 450 \end{array} & \begin{array}{c} \text { Sprint } \\ \text { Basic } \end{array} & \begin{array}{c} \text { Individual } \\ \text { Value } \end{array} & \begin{array}{c} \text { Nationwide } \\ \text { Basic } \end{array} \\ \hline \begin{array}{l} \text { Monthly } \\ \text { minutes } \end{array} & 450 & 200 & 600 & 450 \\ \hline \begin{array}{l} \text { Monthly } \\ \text { cost } \end{array} & \$ 39.99 & \$ 29.99 & \$ 39.99 & \$ 39.99 \\ \hline \begin{array}{l} \text { Plan cost } \\ \text { per minute } \end{array} & & & & \\ \hline \end{array}$$ Find the cost per minute for each plan. Based on your results, which plan should you go with?

Step-by-Step Solution

Answer

Choose the UMGSTIO plan; it has the lowest cost per minute.

Step 1: Understand the Problem

We have a table with four cell phone plans, each with a different provider, number of monthly minutes, and monthly cost. We need to calculate the cost per minute for each plan based on these details.

Step 2: Write the Formula

The formula to find the cost per minute is \( \text{Plan cost per minute} = \frac{\text{Monthly cost}}{\text{Monthly minutes}} \). This formula will allow us to calculate how much each minute costs for each plan.

Step 3: Calculate for Alciu Plan

The Alciu plan has 450 minutes at a cost of $39.99. Using the formula: \( \frac{39.99}{450} = 0.0889 \) dollars per minute.

Step 4: Calculate for Sumple Plan

The Sumple plan has 200 minutes at a cost of $29.99. Using the formula: \( \frac{29.99}{200} = 0.14995 \) dollars per minute.

Step 5: Calculate for UMGSTIO Plan

The UMGSTIO plan has 600 minutes at a cost of $39.99. Using the formula: \( \frac{39.99}{600} = 0.06665 \) dollars per minute.

Step 6: Calculate for VILERIN Plan

The VILERIN plan has 450 minutes at a cost of $39.99. Using the formula: \( \frac{39.99}{450} = 0.0889 \) dollars per minute.

Step 7: Compare Costs and Decide

Comparing the cost per minute: Alciu (0.0889), Sumple (0.14995), UMGSTIO (0.06665), VILERIN (0.0889). The UMGSTIO plan has the lowest cost per minute.

Key Concepts

Cell Phone Plan Comparison

Choosing the best cell phone plan can be tricky, because each provider offers different packages. Various factors such as the number of included monthly minutes and the total monthly cost should be considered.

When comparing cell phone plans, it's crucial to calculate how much you are paying for each minute of talk time. This gives a clear picture of which plan provides the best value. Some plans might offer many extras like text or data but might charge more for simple call durations.

• The Alciu plan offers 450 minutes at a cost of $39.99.
• The Sumple plan includes 200 minutes for $29.99.
• The UMGSTIO plan gives 600 minutes with the same $39.99 cost as Alciu and VILERIN.
• Similarly, VILERIN also offers 450 minutes at the same $39.99 price.

Evaluating these helps find the "cheapest" talk option. In our example, calculating the cost per minute for each plan highlights which is the most cost-effective option.

Formulas in Math

Using formulas in math simplifies complex problems by providing a structured approach to calculations and problem-solving. In the context of cell phone plans, we used a specific formula to determine the cost per minute, crucial for plan comparison.

The formula to find out the cost per minute is:
\[ \text{Plan cost per minute} = \frac{\text{Monthly cost}}{\text{Monthly minutes}} \]
This formula is easy to use; just input the total monthly cost and the number of minutes included in the plan. The outcome is the cost you incur for each minute of usage.

Using this mathematical formula, you can efficiently determine which plan offers the best value for the money. It transforms a decision that might feel overwhelming due to different variables into a simple calculation.

Problem-Solving Steps

Approaching a problem methodically can simplify decision-making. Here's how you can apply structured problem-solving steps to compare cell phone plans.

• Understand the Problem: First, gather information about each plan, including the monthly minutes and costs.
• Use the Formula: Employ the cost per minute formula to standardize the information across plans. This changes complex information into clear data.
• Calculate for Each Plan: Plug the respective values into the formula for each plan. This gives a cost per minute for each option.
• Compare Results: With the cost per minute of each plan known, you can decide which is most cost-effective. Here, the UMGSTIO plan was found to be the cheapest.

Following these steps not only helps in choosing the correct cell phone plan but can also be used in various other real-life decisions. Breaking down a problem into actionable steps leads to better and more efficient decision-making.