## Task 4 - 110624

If one third of Rainer's savings is added to one fifth of this savings, then the sum is exactly 7 marks more than half of his savings.

How many marks has Rainer saved in total?
According to the problem, Rainer possesses a certain amount of money, denoted as \( x \) marks. Then it holds that

\[
\frac{x}{3} + \frac{x}{5} = \frac{x}{2} + 7
\]

From this, after multiplying by 30, we get \( 10x + 6x = 15x + 210 \), and from this \( x = 210 \).

Therefore, Rainer has saved a total of 210 marks.

Solutions of the II. Round 1971 adopted from [5]

### 3.13 XII. Olympiad 1972

### 3.13.1 I. Round 1972, Class 6