Question

Suppose that the cost of sending an international fax is calculated as follows: The service charge is \(\$ 3.00, \$ .20\) per page for the first 10 pages, and \(\$ 0.10\) for each additional page. Design an algorithm that asks the user to enter the number of pages to be faxed. The algorithm then uses the number of pages to be faxed to calculate the amount due.

Short answer

Calculate: $3.00 base + $0.20 per page (1-10) + $0.10 per additional page.

Step-by-step solution

Understand the Problem

The cost structure of sending a fax involves a base service charge of $3.00. For pages 1 through 10, each page costs $0.20. Any pages beyond the 10th are charged at $0.10 per page. Our task is to calculate the total cost based on the number of pages faxed.

Set the Initial Cost Components

Initialize a variable for the service charge, which is $3.00. Then initialize two more variables for the per-page cost up to the first 10 pages ($0.20) and for each additional page beyond the first 10 pages ($0.10).

Collect the User Input

Request input from the user for the total number of pages to be faxed. Store this input in a variable (let's call it `numberOfPages`). Ensure the input is converted to a numerical format (usually an integer) since it will be used in calculations.

Calculate the Total Cost

Implement a series of conditions to calculate the total cost based on `numberOfPages`. - If `numberOfPages` is 10 or less, calculate the cost as: \[ \text{Total Cost} = \\(3.00 + (\text{numberOfPages} \times \\)0.20) \]- If `numberOfPages` is greater than 10, calculate the cost as: \[ \text{Total Cost} = \\(3.00 + (10 \times \\)0.20) + ((\text{numberOfPages} - 10) \times \$0.10) \]

Output the Total Cost

Display the calculated total cost to the user in a format that clearly states the amount due.

Key concepts

Cost Calculation

Calculating the total cost of sending an international fax requires a systematic approach. We begin with a base service charge of \(3.00, applicable regardless of the number of pages. For the next step, we assess how the per-page cost changes depending on the number of pages faxed. If the total number of pages is 10 or fewer, each page costs \)0.20.
The formula is straightforward:

• The cost is \(3.00 + ( ext{numberOfPages} \times 0.20)\).

For cases where more than 10 pages are faxed, the first 10 pages remain at \(0.20 each, and each additional page costs \)0.10. Hence, the cost formula adjusts to:

• \(3.00 + (10 \times 0.20) + (( ext{numberOfPages} - 10) \times 0.10)\)

This method ensures that the cost reflects both the fixed service charge and the variable cost based on page count.

Conditional Statements

Conditional statements are crucial in decision-making within our algorithm. They allow the algorithm to respond appropriately to user input. In this context, we need to distinguish between different ranges of page numbers.

• If the number of pages is less than or equal to 10, the corresponding branch executes, using the formula for up to 10 pages.
• If more than 10 pages are involved, the algorithm follows another path, applying the additional cost structure.

These conditions are set up using simple if-else statements, making the logic clear and the outcome reliable across different scenarios. By organizing different cases of user input this way, we ensure calculations are both efficient and accurate.

User Input Handling

Handling user input is a fundamental step in our algorithm. We begin by prompting the user to enter the number of pages they wish to fax. This data, often input as a string, must be converted to a numerical format suitable for arithmetic operations. This usually means transforming it into an integer.
Handling input cautiously is essential to avoid errors during calculation. We ensure that the number of pages is a valid positive integer. In a robust implementation, we might include checks to handle incorrect input, such as non-numeric or negative values.
This input validation step prevents breakdowns in the algorithm and contributes to a smoother user experience.

International Fax Charges

International fax charges in our example illustrate how different components make up a total cost. The flat service fee of $3.00 is consistent regardless of usage. Meanwhile, the tiered per-page cost reflects usage-dependent pricing.
This approach is common in various billing systems, seeking to balance maintaining a minimum service fee with charging based on actual usage. By understanding this method, you gain insight into pricing models that adapt to different scales of consumption.
The example highlights the importance of breaking down costs into fixed and variable parts, a common approach to designing fair and flexible billing algorithms.