7. In a $5 \times 5$ table, numbers (not necessarily integers) are arranged such that each number is three times smaller than the number in the adjacent cell to the right and twice as large as the number in the adjacent cell below. Find the number in the central cell if it is known that the sum of all numbers in the table is 341.

![](https://cdn.mathpix.com/cropped/2024_05_06_581b4976cdd354ac9814g-3.jpg?height=507&width=520&top_left_y=2010&top_left_x=323)
Answer: $\frac{36}{11}$. Solution. Let the number in the lower left corner be $x$. We get the equation $x(1+2+4+8+16)(1+3+9+27+81)=341$, from which $x=\frac{1}{11}$. The number in the center is $36 x=\frac{36}{11}$.