Problem 12 - College Algebra

Question

For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of \(\$ 20\) and charges of \(\$ .05 / \mathrm{min}\) for calls. Company \(\mathrm{B}\) has a monthly fee of \(\$ 5\) and charges \(\$ .10 / \mathrm{min}\) for calls. If the person makes a monthly average of 200 min of calls, which plan should for the person choose?

Step-by-Step Solution

Answer

Company B is cheaper with a total cost of \( \$25 \).

Step 1: Calculate Total Cost for Company A

To calculate the total cost for Company A, add the monthly fee to the cost of the minutes used. Company A charges \( \\(20 \) as a monthly fee, and \( \\)0.05 \) per minute. For 200 minutes, the cost is \( 200 \times 0.05 = \\(10 \). Therefore, the total monthly cost for Company A is: \( \\)20 + \\(10 = \\)30 \).

Step 2: Calculate Total Cost for Company B

Company B charges \( \\(5 \) monthly and \( \\)0.10 \) per minute. For 200 minutes, calculate the call cost: \( 200 \times 0.10 = \\(20 \). Therefore, the total monthly cost for Company B is: \( \\)5 + \\(20 = \\)25 \).

Step 3: Compare the Costs

Now compare the total costs calculated for each company. Company A's total monthly cost is \( \\(30 \), while Company B's total monthly cost is \( \\)25 \).

Step 4: Determine the Cheaper Option

Since \( \\(25 \), the cost of Company B, is less than \( \\)30 \), the cost of Company A, the person should choose Company B.

Key Concepts

Telephone plans

When it comes to choosing a telephone plan, it is essential to consider both fixed costs like monthly fees and variable costs like charges per minute of calls. Different companies often provide various plans with distinct pricing structures.
In our exercise, we are looking at two telephone plans from Company A and Company B. Company A offers a plan with a higher monthly fee but a lower cost per minute, whereas Company B provides a plan with a lower monthly fee but a higher cost per minute.
It is crucial to understand your average usage patterns, like how many minutes you talk on the phone each month, to choose the best plan suited for your needs. Once you have this data, calculating the expected monthly costs for each plan can guide you in making an economical decision.

Step-by-step solution

Breaking down a problem into smaller, manageable steps is key in tackling math or finance-related questions. For this exercise, a step-by-step approach helps in making sense of the cost comparison between two phone plans.
Start by calculating the total monthly cost for each plan separately. For Company A, calculate the cost by adding the monthly fee and the cost of minutes used. Repeat the same for Company B. Once you have both costs, compare them directly.
Following a structured method not only aids in achieving an accurate solution but also enhances your understanding of the underlying process. This technique can be applied to various real-life scenarios where comparing costs or benefits is necessary.

Monthly fee calculation

Monthly fee calculation involves determining the total amount you will spend on a service in one month, based on its fixed charges and your usage. In this exercise, we consider two main components of the fee:

• The fixed monthly fee, which is a constant charge irrespective of usage.
• The charge per minute for calls, which varies depending on your call usage.

For Company A, this calculation is done by adding the monthly fee of $20 to the cost derived from your average monthly call minutes (200 minutes x $0.05 per minute). Similarly, for Company B, add the monthly fee of $5 to the cost from your average call minutes (200 minutes x $0.10 per minute).
Understanding how to calculate these fees can lead to better financial decision-making when comparing different service plans, ensuring that you choose the most cost-effective option.