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When you encounter a percentage discount, it refers to a reduction from the item's normal price. This reduction is expressed as a percentage of the original price. Understanding percentage discounts is crucial for calculating sale prices effectively. Let's break it down:

• First, identify the original price of the item. In our case, it is the CD priced at \(\\(13.95\).
• Next, note the percentage being deducted. Here, it's \(15\%\).
• To find out how much money you save because of this discount, convert the percentage to a decimal by dividing by 100. Thus, \(15\%\) becomes \(0.15\).
• Multiply this decimal by the original price to find the discount in dollars. For the example, the calculation would be \(13.95 \times 0.15\), which gives an approximate savings of \(\\)2.09\).

Calculating a percentage discount allows you to determine the instant dollar amount being deducted from a purchase, providing a tangible sense of savings.

After finding out the discount, the next step is to calculate an item's sale price. The sale price is what you end up paying after the discount is deducted from the original price.

• Begin with the original price of an item or product, as in our example where the original price is \(\\(13.95\).
• Subtract the determined discount amount from this original price to find the sale price.
• For our CD, the subtraction would be \(13.95 - 2.09\), equating to a sale price of \(\\)11.86\).

Knowing how to calculate the sale price equips you with the ability to quickly determine your actual payment amount after discounts, enabling budgeting and intelligent shopping decisions. It’s essential to perform both the multiplication and subtraction correctly to reach an accurate result.

In the context of discount calculations, mathematical equations play a pivotal role. They provide a structured way to solve real-world problems like discounts and sale prices step-by-step. The direct variation equation specifically helps us in quickly determining the sale price given any original price and discount percentage.

The general direct variation equation for a scenario like this is:
\[\text{Sale Price} = \text{Original Price} - (\text{Original Price} \times \frac{\text{Discount Percentage}}{100})\]
This formula breaks the task into manageable parts:

• By calculating \(\text{Original Price} \times \frac{\text{Discount Percentage}}{100}\), we find the discount.
• Subtracting this discount from the Original Price gives the Sale Price. In our example, it simplifies to: \(13.95 - (13.95 \times 0.15)\).
• This expression guides you in seeing how each part contributes to finding the sale price, reinforcing understanding through consistent practice.

Understanding these types of equations is valuable because it not only aids in solving discount problems but also hones algebraic thinking applicable across various mathematical tasks.