To find the original price of the item, you can use the formula for calculating the price after a discount:

$\text{Price after discount} = \text{Original Price} \times (1 - \text{Discount Rate})$

Given:

• Price after discount = 75.00
• Discount rate = 40% or 0.40

Now, let the original price be $x$.

$75.00 = x \times (1 - 0.40)$ $75.00 = x \times 0.60$

To solve for $x$, divide both sides of the equation by 0.60:

$x = \frac{75.00}{0.60}$ $x = 125.00$

So, the original price of the item was $125.00.

Would you like more details or have any questions?

Here are 5 related questions to further explore:

1. How would the original price change if the discount was 30% instead of 40%?
2. If an additional tax of 10% was applied after the discount, what would the final price be?
3. How can you express the original price in terms of the discounted price and discount rate?
4. What is the formula to calculate the percentage discount given the original and discounted prices?
5. How would the calculation differ if multiple discounts were applied successively?

Tip: When calculating discounts, always ensure you're working with percentages as decimals (e.g., 40% = 0.40) for accurate results.