Dwayne wants to buy a bowling ball that has a price of $120. As a member of a bowling league, he is entitled to a 15% discount off the price of the bowling ball. He will also have to pay 6% sales tax on the discounted price of the bowling ball. Dwayne thinks that the final price of the bowling ball can be determined by taking 9% off the original price. Is Dwayne correct? Support your answer with a detailed explanation.