Pet World offers a \(15 \%\) discount to senior citizens. Write a pseudocode algorithm for a program that inputs the amount of a sale, then calculates and displays both the amount the customer saves and the amount they must pay.

Programming logic is a foundational component that drives the behavior of computer programs. It involves a sequence of operations based on a set of rules or principles, guiding the program to perform specific tasks based on given inputs. When writing pseudocode, or a simplified representation of programming code, the programmer sketches out the structural logic without the complexity of syntax rules from any specific programming language.

Pseudocode allows you to focus on the algorithm's steps – such as input handling, process flow, and output generation – without getting bogged down by the intricacies of a coding language. It's like writing out a recipe before cooking a meal; you're planning the steps needed to reach the desired outcome. Good programming logic requires that these steps are clear, unambiguous, and arranged in the correct sequence to produce the correct output.

A discount calculation is a mathematical operation where a percentage reduction is applied to a price. Understanding how discounts work is important not only in everyday life, such as shopping, but also in programming when you want to include such operations in your application.

For instance, Pet World offers a 15% discount to senior citizens. In a programming context, this calculation would typically go as follows: a 15% discount on an item worth \( \(100 \) means a saving of \( \)15 \), hence the item's final price is \( $85 \). The standard formula used is:
\[ DiscountAmount = \frac{PercentDiscount}{100} \times OriginalAmount \]
Therefore, calculating discounts is a vital function in commerce-related applications and requires understanding and applying the correct arithmetic operations to determine the amount saved and the final price to be paid.

User input is a crucial part of many programs, allowing for dynamic processing based on the information provided by the user. In the context of a pseudocode algorithm designed for calculating discounts, user input would typically be the first step in the program. Here, the program requests the original amount of the sale from the user, setting off the chain of calculations that follow.

Proper handling of user input is essential to ensure the program functions as intended. This means your program should not only accept the input provided by the user but also verify that it's in the correct format and within the expected range. For instance, in a discount calculation program, the application should check that the user enters a numeric value and that it's a positive amount before proceeding with calculations. This step helps in avoiding errors and improving the user experience.