Task B-2.3. In a certain city, there are 10 restaurants and $n$ theaters. A group of tourists spent several days in this city. During their stay, they visited restaurants and theaters. At the end of their stay, they found that each restaurant had been visited by 4 tourists, and each theater had 6 tourists. If each tourist visited exactly 5 restaurants and 3 theaters, determine how many theaters there are in the city.
## Solution.

Let $t$ be the total number of tourists. The number of visits to restaurants is

$$
t \cdot 5 = 4 \cdot 10
$$

Then $t = 8$.

Similarly, the number of visits to theaters is

$$
t \cdot 3 = 6 \cdot n
$$

It follows that $t = 2n$, or $n = 4$, which means there are exactly 4 theaters in the city.