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Omni-MATH / At the end of the year 2000, Steve had 100 and Wayne had 10000. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne…

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problem

At the end of the year 2000, Steve had $100\$100 and Wayne had $10000\$10000. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?
Plain-text mathematical notation (without MathML)
At the end of the year 2000, Steve had $100 and Wayne had $10000. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?
Original LaTeX notation
At the end of the year 2000, Steve had $\$100$ and Wayne had $\$10000$. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?

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