# RE2 | perplexity/sonar-pro | run 1

## Prompt

After a 20% discount, a jacket costs $40. What was the original price? Show your work.

## Response

The jacket’s original price was **$50**. This comes from reversing the 20% discount to find the pre-discount amount.

## Step-by-step work

Let \(x\) be the **original price** of the jacket.

A **20% discount** means the customer pays **80% of the original price** (because \(100\% - 20\% = 80\% = 0.80\)). This relationship is standard in discount formulas:  
\[ \text{Sale price} = \text{Original price} \times (1 - \text{Discount \%}/100) \][Omni Calculator – Price Before Discount](https://www.omnicalculator.com/finance/percentage-discount)[Calculatorsoup – List Price Formula](https://www.calculatorsoup.com/calculators/financial/discount-calculator.php)

So:
\[
0.80x = 40
\]

Now solve for \(x\):

\[
x = \frac{40}{0.80}
\]

\[
x = 50
\]

Therefore, the **original price** of the jacket was **$50**.

You can check the answer:
- 20% of $50 is \(0.20 \times 50 = 10\).
- $50 − $10 = $40, which matches the given discounted price.

Would you like to see how to set this up using a proportion instead of an equation?
