Final answer:
Raul is correct; to find the final price after a 15% discount and a 6% sales tax, you cannot simply subtract 9% from the original price. The discounted price is calculated first and then the sales tax is added to that discounted price, resulting in an overall effect of a 9.9% reduction from the original price.
Step-by-step explanation:
The calculation of the final price of a product after applying a discount and then adding sales tax cannot be represented by a single percentage reduction from the original price. Let's break down the correct steps to find the final price of the bowling ball Dwayne wants to purchase.
Calculating the Discounted Price:
- Start with the original price of the bowling ball, let's call it 'x'.
- Apply the 15% discount. The discount amount will be 0.15x.
- Subtract the discount from the original price: x - 0.15x = 0.85x. This is the discounted price.
Applying Sales Tax:
- The 6% sales tax applies to the discounted price, not the original price. The sales tax amount will be 0.06 * 0.85x.
- Add this tax to the discounted price: 0.85x + (0.06 * 0.85x).
When we do the math, 0.06 * 0.85x equals 0.051x, so adding this to 0.85x gives us 0.901x, which represents a 9.9% reduction from the original price, not 9% as Dwayne thought.
Thus, Raul is correct. To calculate the final price, one cannot simply subtract 9% from the original price. Instead, the process involves first reducing the price by the discount and then adding back the sales tax to the reduced price.