A product’s price was first increased by 30% and then decreased by 20%. If the final price is $84, what was the original price of the product?

Let's solve the problem step-by-step to find the original price of the product.

1. **Let the original price be** $ x $.

2. **Price after a 30% increase**:
   \[
   \text{Increased Price} = x + 0.3x = 1.3x
   \]

3. **Price after a 20% decrease**:
   The decreased price from $ 1.3x $ is given by reducing it by 20%, which is equivalent to multiplying by $ 0.8 $.

   \[
   \text{Final Price} = 1.3x \times 0.8
   \]

4. **We know the final price is $84**:
   \[
   1.3x \times 0.8 = 84
   \]

5. **Solve for $ x $**:
   \[
   1.04x = 84
   \]

   \[
   x = \frac{84}{1.04}
   \]

   \[
   x = 80.77
   \]

Thus, the original price of the product was **$80.77**.

Would you like more details, or do you have any questions? 

Here are 5 related questions to expand your understanding:

1. What would be the final price if the original price was $100 instead?
2. How would a sequence of a 20% increase followed by a 30% decrease affect the final price?
3. If the price was increased by 50% and then decreased by 50%, what would the final price be as a percentage of the original price?
4. How would the final price change if the decrease was 10% instead of 20% after the 30% increase?
5. Can you generalize the formula for any percentage increase followed by any percentage decrease?

**Tip**: Always convert percentages to decimals when performing calculations to ensure accuracy.

Learn how to calculate the original price of a product after it was first increased by 30% and then decreased by 20%. Detailed step-by-step solution included, with the final price given as $84.

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