Vinny weighed 300 pounds then lost 20 pounds in the first month of his diet. He continued his diet but each month, he lost half as much weight as he had lost in the previous month. At the start of the fifth month of his diet, he worked harder to lose extra weight then decided to end his diet. If Vinny weighed 250.5 pounds at the end of his diet, how many pounds did he lose throughout the fifth month? Let's think first. Chain of thought:
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In the second month, Vinny lost half as much as he had the first month, so he lost 20 pounds / 2 = 10 pounds. In the third month, he again lost half as much which was 10 pounds / 2 = 5 pounds. And in the fourth month, he lost 5 pounds / 2 = 2.5 pounds. So in total, Vinny lost 20 + 10 + 5 + 2.5 = 37.5 pounds in the first four months. Over his entire diet, he had lost 300 – 250.5 = 49.5 pounds. So in the fifth month, Vinny must have lost 49.5 pounds total loss – 37.5 pounds loss in the first four months = 12 pounds.
Therefore, the answer is 12.
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