Florián was thinking about what bouquet he would have tied for his mom for Mother's Day. In the florist's, according to the price list, he calculated that whether he buys 5 classic gerberas or 7 mini gerberas, the bouquet, when supplemented with a decorative ribbon, would cost the same, which is 295 crowns. However, if he bought only 2 mini gerberas and 1 classic gerbera without any additional items, he would pay 102 crowns.

How much does one ribbon cost? 

(L. Šimůnek)
From the assignment, it follows that 5 classic gerberas cost the same as 7 minigerberas, meaning that the price of a classic gerbera and the price of a minigerbera are in the ratio of $7: 5$. If we represent the price of a classic gerbera with 7 equal parts, the price of a minigerbera will correspond to 5 such parts.

The cost of purchasing 2 minigerberas and 1 classic gerbera represents $2 \cdot 5 + 7 = 17$ of these parts, so 1 part therefore corresponds to the amount 102 : 17 = 6 crowns. Five classic gerberas, or seven minigerberas, cost $5 \cdot 7 \cdot 6 = 210$ crowns. The price of the ribbon is $295 - 210 = 85$ crowns.

Evaluation. 2 points for determining that the prices of a classic gerbera and a minigerbera are in the ratio of 7 : $5 ; 2$ points for determining the corresponding equation $17 d = 102 ; 2$ points for deriving the price of the ribbon $(d = 6, 295 - 5 \cdot 7 \cdot d = 85)$.