Finding the Original Price of a Perfume Discounted 25% and Sold for $27

When a perfume is discounted by 25% and sold for $27, finding its original price involves a bit of basic math. Let's break down the process step-by-step to determine the original price before the discount was applied.

Step 1: Understanding the Discount A 25% discount means that the perfume is being sold at 75% of its original price. This is because 100% - 25% = 75%.

Step 2: Setting Up the Equation Let $P$P represent the original price of the perfume. After a 25% discount, the price is reduced to 75% of $P$P. So, the equation to represent the sale price is: $0.75P=27$0.75P=27

Step 3: Solving for the Original Price To find $P$P, divide both sides of the equation by 0.75: $P=\frac{27}{0.75}$P=0.7527​

Step 4: Performing the Calculation Using basic division: $\frac{27}{0.75}=36$0.7527​=36

So, the original price of the perfume before the discount was $36.

Verification To verify, calculate 25% of $36 and subtract it from $36:

• 25% of $36 is $0.25\times 36=9$0.25×36=9
• Subtracting $9 from $36 gives us $27, which confirms the sale price.

Conclusion The original price of the perfume was $36. This calculation confirms that with a 25% discount leading to a sale price of $27, the starting price was indeed $36.