## 50. Math Puzzle $7 / 69$

"To solve a question that relates to numbers and abstract relationships of quantities, one merely needs to translate the problem from the mother tongue into the language of algebra," wrote the famous Newton in his textbook "Arithmetica universalis". You are to perform such a translation for one of Newton's problems:

"A merchant possessed a certain sum of money. In the first year, he spent 100 pounds. To the remaining sum, he added a third of it.

In the next year, he spent another 100 pounds and increased the remaining sum by a third of it. In the third year, he spent another 100 pounds. He then added a third of the remainder to it and thus doubled his initial capital."
$$
\begin{aligned}
(x-100)+\frac{x-100}{3} & =\frac{4 x-400}{3} \\
\frac{4 x-400}{3}-100 & =\frac{4 x-700}{3} \\
\frac{4 x-700}{3}+\frac{4 x-700}{9} & =\frac{16 x-2800}{9} \\
\frac{16 x-3700}{9}+\frac{16 x-3700}{27} & =\frac{64 x-14800}{27} \\
\frac{64 x-14800}{27}= & 2 x
\end{aligned}
$$

The solution to the equation is 1480, which means the merchant had an initial capital of 1480 pounds.