Shapovalov A.V.

The price of a standard lunch at the "Buratino" tavern depends only on the day of the week. Anya dined for 10 consecutive days starting from July 10 and paid 70 soldo. Vanya also paid 70 soldo for 12 meals starting from July 12. Tanya paid 100 soldo for 20 meals starting from July 20. How much will Sanya pay for 24 meals starting from July 24?
Let's create a calendar from July 10 to August 16, conditionally considering August 10 as the first day of the week. Each row of the calendar corresponds to the same day of the week (see Fig. a). Let the cost of lunch on the first day of the week be $a_{1}$ soldo, on the second day $-a_{2}$ soldo, ..., on the seventh day $-a_{7}$ soldo. The total cost of all lunches for the week is denoted as $P = a_{1} + a_{2} + \ldots + a_{7}$. Let's mark on our calendar the days when Anya (see Fig. b), Vanya (see Fig. c), and Tanya (see Fig. d) had lunch.

| 10 17 | 243 |  | 7 14 | 10 | 17 | 24 |  | 7 | 14 | 10 | 17 | 24 | 31 | 7 | 14 | 10 | 7 2 | 31 | 7 | 14 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 11 18 | 25 | 1 | 8 15 | 11 | 18 | 25 | 1 | 8 | 15 | 11 | 18 | 25 | 1 | 8 | 15 | 11 | $18 \mid 2$ | $\overline{1}$ | 8 | 15 |
| 12 19 | 26 | $C_{1}$ | 9 16 | 12 | 19 | 26 | 2 | 9 | 16 | 12 | 19 | 26 | 2 | 9 | 16 | 12 | 19 2 | 2 | 9 | 16 |
| 13 20 | 27 |  1 | 10 | 13 | 20 | 27 | 3 | 10 |  | 13 | 20 | 27 | 3 | 10 |  | 13 | $20 \mid 2$ | 3 | 10 |  |
| 14 21 | 28 | 4 1 | 11 | 14 | 21 | 28 | 4 | 11 |  | ![](https://cdn.mathpix.com/cropped/2024_05_06_62351a5cb646b08ac6fbg-10.jpg?height=55&width=78&top_left_y=209&top_left_x=1043) | 21 | 28 | 4 | 11 |  | 14 | ![](https://cdn.mathpix.com/cropped/2024_05_06_62351a5cb646b08ac6fbg-10.jpg?height=55&width=92&top_left_y=209&top_left_x=1585) | 4 | 11 |  |
| 15 22 | 29 | 5 1 | 12 | \|15 | 22 | 29 | 5 | 12 |  | ![](https://cdn.mathpix.com/cropped/2024_05_06_62351a5cb646b08ac6fbg-10.jpg?height=55&width=78&top_left_y=259&top_left_x=1043) | 22 | 29 | 5 | 12 |  |  | ![](https://cdn.mathpix.com/cropped/2024_05_06_62351a5cb646b08ac6fbg-10.jpg?height=55&width=87&top_left_y=259&top_left_x=1585) | 5 | 12 |  |
| 16 23 | 30 | 6 1 |  | 16 |  |  | 6 | 13 |  |  |  | 30 | 6 | 13 |  |  |  | $\overline{6}$ | 13 |  |
|  | $\mathrm{Pn}$ |  |  |  |  | n上 |  |  |  |  |  |  |  |  |  |  |  |  |  |

In total, they had lunch six times on each day of the week and paid $70 + 70 + 100 = 240$ soldo. This means that the cost of seven consecutive lunches (one each day of the week) is $240 / 6 = 40$ soldo. Now, let's mark the days when Sanya had lunch (see Fig. d). Notice that he had lunch on the same days as Anya, plus two more weeks. Therefore, Sanya should pay $70 + 2 \cdot 40 = 150$ soldo.

| 10 | 17 | 24 | 31 | 7 | 14 |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 11 | 18 | 25 | 1 | 8 | 15 |
| 12 | 19 | 26 | 2 | 9 | 16 |
| 13 | 20 | 27 | 3 | 10 |  |
| 14 | 21 | 28 | 4 | 11 |  |
| 15 | 22 | 29 | 5 | 12 |  |
| 16 | 23 | 30 | 6 | 13 |  |

Fig. d

## Answer

150 soldo.