13.369. Around the house, lindens and birches are planted, and their total number is more than 14. If the number of lindens is doubled and the number of birches is increased by 18, then the number of birches will be greater than the number of lindens. If, however, the number of birches is doubled without changing the number of lindens, then the number of lindens will now be greater than the number of birches. How many lindens and how many birches were planted?

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-1224.jpg?height=494&width=570&top_left_y=1263&top_left_x=706)

Fig. 13.20
Solution.

Let $x, y$ be the number of lindens and birches, respectively. According to the condition, we have the system of inequalities $\left\{\begin{array}{l}x+y>14, \\ y+18>2 x, \\ x>2 y .\end{array}\right.$

Construct the lines $x+y=14$ (1), $y+18=2 x$ (2), $x=2 y$ (3). From Fig. 13.20, it is clear that the point ( $11 ; 5$ ) is the only point with natural coordinates that lies inside the triangle $A B C$, i.e., satisfies our system of inequalities.

Answer: 11 lindens and 5 birches.