9.1. In a supermarket, there are two types of fruit sets for sale. The first type of set consists of 3 apples and 15 oranges and costs 360 rubles. The second type of set consists of 20 apples and 5 oranges and costs 500 rubles. Fruits are sold only in sets, and sets cannot be divided. Seryozha came to the supermarket and wants to buy an equal number of apples and oranges. What is the smallest amount of money he will have to spend, if he cannot leave without buying anything?
Solution: Let Sergey buy $x$ sets of the first type and $y$ sets of the second type. Then he bought $3x + 20y$ apples and $15x + 5y$ oranges. From the problem's condition, it follows that these numbers are equal, that is, $15y = 12x$ or $5y = 4x$. The smaller $y$ is, the smaller $x$ is, and the smaller the amount paid. The smallest natural $y$ is 4, then $x = 5$, and the amount spent in rubles is $5 \cdot 360 + 4 \cdot 500 = 3800$.

Answer: 3800 rubles.

Recommendations for checking:

| present in the work | points |
| :--- | :--- |
| Correct justified answer | 7 points |
| A correct approach but an incorrect answer due to arithmetic errors | 6 points |
| It is shown that 3800 rubles can be spent, but it is not shown that a smaller amount cannot be spent | 2 points |
| Examples of purchases costing more than 3800 rubles | 0 points |