Three gardeners invited a ploughman to plough their plots. The ploughman charged the same price per square meter for all of them. In total, the gardeners paid 570 Kč.

Two of the plots were square, one was rectangular. The area of the rectangular plot was 6 ares and one of its sides measured $20 \mathrm{~m}$. The side length of one of the square plots was the same as the length of the rectangular plot, and the side length of the other square plot was the same as the width of the rectangular plot.

How much did each of the gardeners pay for the ploughing?

(M. Krejčová)
The area of the rectangular plot was 6 ares, i.e., $600 \mathrm{~m}^{2}$. One of its sides measured $20 \mathrm{~m}$, so the other side measured $600: 20=30(\mathrm{~m})$. The side of one square plot was $20 \mathrm{~m}$ long, its area was $20 \cdot 20=400\left(\mathrm{~m}^{2}\right)$, i.e., 4 ares. The side of the second square plot was $30 \mathrm{~m}$ long, its area was $30 \cdot 30=900\left(\mathrm{~m}^{2}\right)$, i.e., 9 ares.

All three plots together had $6+4+9=19($ ares). The gardeners paid a total of 570 Kč, so plowing one are cost $570: 19=30$ Kč.

The gardener with the rectangular plot paid $6 \cdot 30=180$ Kč, the gardener with the smaller square plot paid $4 \cdot 30=120$ Kč, and the gardener with the larger square plot paid $9 \cdot 30=270 \mathrm{Kč.}$

Scoring proposal. 1 point for the second side of the rectangular plot; 1 point for the areas of the square plots; 2 points for the unit price of plowing; 2 points for the payments of the individual gardeners.