## Task 4 - 100524

A group of young mathematicians went on an excursion. Each participant paid 1.50 marks for travel expenses. When paying for the collective ticket, a remainder of 1.10 marks was left.

If each participant had paid 1.40 marks, there would have been a shortage of 1.10 marks to cover the cost of the collective ticket.

Determine the number of participants in this excursion! How much money did each of these participants receive back when the excess amount paid was evenly distributed among them?
Given that with a participant contribution of 1.40 Marks, exactly 1.10 Marks were missing, and with a contribution of 1.50 Marks, exactly 1.10 Marks were too much, the collected money would have been exactly double the cost of one collection ticket if each participant had paid 2.90 Marks.

Consequently, the exact cost of one collection ticket would have been collected if each participant had paid 1.45 Marks. Thus, each participant had paid 0.05 Marks too much.

This amount was refunded to each participant. Since $110: 5=22$, there were 22 young mathematicians participating in this excursion.

Solutions of the II. Round 1970 taken from [5]

### 2.12 XI. Olympiad 1971

### 2.12.1 I. Round 1971, Class 5