1. **State the problem:** You bought a sweatshirt with a 40% off coupon and paid 18 after the discount. We need to find the original price. 2. **Formula and explanation:** The price paid after discount is given by: $$\text{Price Paid} = \text{Original Price} - (\text{Discount} \times \text{Original Price})$$ Since the discount is 40%, or 0.40, this can be rewritten as: $$18 = \text{Original Price} \times (1 - 0.40)$$ 3. **Simplify the equation:** $$18 = \text{Original Price} \times 0.60$$ 4. **Solve for Original Price:** Divide both sides by 0.60: $$\text{Original Price} = \frac{18}{0.60}$$ Show canceling common factors: $$\text{Original Price} = \frac{18}{\cancel{0.60}} \times \frac{\cancel{1}}{1}$$ 5. **Calculate the value:** $$\text{Original Price} = 30$$ 6. **Answer:** The original price of the sweatshirt was 30. This means before applying the 40% discount, the sweatshirt cost 30.