Mary tried to improve her health by changing her diet, but her weight bounced like a yo-yo. At first, she dropped a dozen pounds. Then, she added back twice the weight that she initially lost. Then, she dropped three times more weight than she initially had lost. But finally, she gained back half of a dozen pounds. If she weighed 99 pounds at the start of her change in diet, what was her final weight, in pounds? Give me reasons, before answering the question
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Since Mary first weighed 99 pounds, after she dropped a dozen pounds she weighed 99 - 12 = 87 pounds. Twice the weight she initially lost is 12 * 2 = 24 pounds. So, when she added back twice the weight that she initially lost, her weight jumped to 87 + 24 = 111 pounds. Three times more than she initially had lost is 12 * 3 = 36 pounds. Therefore, when Mary lost 3 times more than she initially lost, her weight dropped to 111 - 36 = 75 pounds. Finally, when Mary gained back half of a dozen pounds, her final weight was 75 + 6 = 81 pounds. So the final answer is 81.
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