## Task 4 - 070624

Of the participants from a school in a district at the 1st stage of the Mathematics Olympiad, exactly $\frac{3}{40}$ were delegated to the 2nd stage. Of these students, exactly $\frac{2}{9}$ received awards or certificates of recognition at the 2nd stage (District Olympiad).

One student received a first prize in his grade, exactly one other student received a second prize in his grade, exactly two others received third prizes. In addition, exactly four other students from this school were awarded certificates of recognition for particularly good solutions to a problem.

Give the total number of participants from this school at the 1st stage of the Mathematics Olympiad!
Students with prizes or letters of recognition:

8 students $=\frac{2}{9}$ of the participants in the 2nd stage. This implies:

4 students $=\frac{4}{9}$ of the participants in the 2nd stage and

36 students $=\frac{9}{9}$, (which are all participants of this school in the 2nd stage)

According to the problem, it also holds that: 36 students $=\frac{3}{40}$ of the participants in the 1st stage, so 480 students $=\frac{40}{40}$ (which are all participants of this school in the 1st stage). Exactly 480 students from this school participated in the 1st stage of the Mathematics Olympiad.

Solutions of the 2nd round 1967 taken from [5]

### 3.9 VIII. Olympiad 1968

### 3.9.1 1st Round 1968, Class 6