Question

Suppose that the cost of sending an international fax is calculated as follows: Service charges \(\$ 3.00 ; \$ .20\) 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 the cost based on the number of pages, then add a $3.00 service charge.

Step-by-step solution

Understand the Problem

The problem consists of determining the total cost of sending an international fax given a basic service charge and a cost for the number of pages to be faxed. The service charge is a constant fee, and there is a variable cost depending on the number of pages.

Initialize Variables

Define three variables: a fixed service charge of $3.00, a charge per page for the first 10 pages ($0.20 per page), and a charge per page for additional pages beyond the first 10 ($0.10 per page).

Identify Input

Determine the input required from the user, which in this case is the number of pages to be faxed, represented as a variable 'num_pages'.

Calculate Cost for Pages

If the number of pages is less than or equal to 10, multiply the number of pages by $0.20 to calculate the variable cost. If it exceeds 10, multiply the first 10 pages by $0.20, and multiply the remainder by $0.10.

Calculate Total Cost

Add the fixed service charge of $3.00 to the calculated cost for pages from Step 4 to get the total cost of the fax.

Output the Result

Output the total cost calculated in Step 5 as the amount due for sending the fax.

Key concepts

Cost Calculation

Calculating the cost of an international fax involves a few simple arithmetic operations. The main components are a fixed service charge and a variable cost based on the number of pages faxed. Here's how it breaks down:

• Fixed Service Charge: This is a constant amount charged for every fax. In this case, it's $3.00.
• Variable Cost for Pages: There are two tiers for this cost: the first 10 pages cost $0.20 each, and any additional pages cost $0.10 each.

To compute the total cost, start by multiplying the number of pages by their respective costs based on these tiers. Once you have the page cost, simply add the fixed service charge of $3.00 to get the total. It's a straightforward calculation, but paying attention to these charges ensures an accurate total.

User Input Handling

Handling user input is a critical step in this algorithm. This is where we ask the user for the number of pages they want to fax. Ensuring that the input is correctly captured and valid is important for accurate calculations.

• Prompting for Input: Clearly ask the user to enter the number of pages they wish to fax. This can be done using a simple print statement or dialog box, depending on the programming environment.
• Validating Input: Once the input is received, check that it is a valid number. This means ensuring it's a non-negative integer as you can't fax a negative number of pages.

Proper user input handling increases the reliability of your algorithm by preventing errors before they interrupt the calculation process.

Conditional Logic

Conditional logic plays a vital role in determining the cost when faxing more than ten pages. This involves using decision-making structures to apply the correct pricing tiers.

• If-Else Statements: Use these to decide if the number of pages is more or less than ten.
• Logical Flow: If the pages are 10 or less, the cost is calculated simply by multiplying with $0.20. For more than 10 pages, the first 10 pages are priced at $0.20 each, and the rest are priced at $0.10.

By using conditional logic, you efficiently manage cases where the pricing model shifts, ensuring that users are charged accurately based on their fax requirements.