## Task 3 - 150613

In the year 1770, the Swiss mathematician Leonhard Euler published a textbook on algebra that was one of the most widely read algebra books for more than 100 years. A problem from this textbook reads:

The number 25 is to be divided into two summands such that the larger of the two summands is 49 times as large as the other.

Investigate whether such a decomposition is possible, and determine, if this is the case, the two summands that occur!
If such a decomposition is possible, then for it:

If we denote the smaller of the two summands by $x$, then the larger one is $49x$, and it holds that $x + 49x = 25$, from which we obtain $x = \frac{1}{2}$.

Therefore, the only decomposition that can have the required properties is one where the smaller summand is $\frac{1}{2}$ and the larger one is $49 \cdot \frac{1}{2} = \frac{49}{2}$.

This is indeed a decomposition of the desired type; for these two summands, $\frac{1}{2} + \frac{49}{2} = 25$.