1. **Stating the problem:** A jacket is discounted 40%, then an additional 25%, and after a 15% tax, the final price is 103.50. We need to find: a. The original price. b. The total percent discount. 2. **Formula and rules:** - Let the original price be $P$. - After a 40% discount, the price becomes $P \times (1 - 0.40) = 0.60P$. - Then a 25% discount on the reduced price: $0.60P \times (1 - 0.25) = 0.60P \times 0.75 = 0.45P$. - After applying 15% tax, the final price is $0.45P \times (1 + 0.15) = 0.45P \times 1.15 = 0.5175P$. 3. **Calculate the original price:** Given final price $= 103.50$, so: $$ 0.5175P = 103.50 $$ Divide both sides by 0.5175: $$ P = \frac{103.50}{0.5175} $$ Show cancellation: $$ P = \frac{103.50}{\cancel{0.5175}} \times \frac{\cancel{1}}{1} = 200 $$ So, the original price is $200$. 4. **Calculate total percent discount:** The total discount factor is $0.45$ (since $0.45P$ is the price before tax). Total discount percent = $(1 - 0.45) \times 100\% = 0.55 \times 100\% = 55\%$. **Final answers:** - a. Original price = $200$ - b. Total percent discount = $55\%$