## Task 1 - 050721

At the Rostock public transport companies, you can buy tram tickets for adults at the following prices:

(1) A ticket from the ticket machine for 0.20 MDN

(2) A card with 6 fare sections for 1.00 MDN

(3) A block of 50 tickets for 7.50 MDN (The validity period is unlimited)

(4) A monthly pass for unlimited rides for 10.00 MDN

What is the minimum number of trips (per month) for which the monthly pass is the cheapest option for a person?
A tram ride costs in case (1) 20 Pfennig, in case (2) $16 \frac{2}{3}$ Pfennig, in case (3) 15 Pfennig. In case (3), $x$ rides in a month cost exactly $15 \cdot x$ Pfennig, while in case (4) they cost exactly 1000 Pfennig.

Therefore, the monthly ticket is the cheapest for $x$ rides exactly when $15 \cdot x \geq 1000$; that is, with 67 and more rides per month, the monthly ticket is the cheapest, and not with fewer rides.

The number sought is therefore 67.