Final answer:
To solve for the original CD cost before the 20% discount, set up the equation x - 0.20x = $9.99, and solve for x to find that the original price equals $9.99 divided by 0.80.
Step-by-step explanation:
To determine the original cost of the CD before the 20% discount, we utilize the given sale price of $9.99. Let's denote the original price as x. The proportion can be set up as \(x - 0.20x = $9.99\), representing the original price minus 20% of the original price equaling the sale price.
Simplifying the equation yields \(0.80x = $9.99\). To isolate x, the original price, we divide both sides of the equation by 0.80. The calculation is \(x = $9.99 / 0.80\).
By performing this division, we can find the original price of the CD. The result gives us the original cost before the 20% discount was applied. This approach showcases the use of proportions and algebraic manipulation to solve real-world problems involving discounts.
In this context, understanding how to reverse the effects of a percentage discount is crucial for consumers and retailers alike. It enables individuals to discern the original value of a product, providing transparency in pricing. Additionally, this mathematical process underscores the importance of algebra in practical scenarios, illustrating its applicability in solving problems related to finance and commerce. Overall, this method equips individuals with the skills to navigate and comprehend pricing structures in the realm of discounts and sales.