Problem 7.5. A rectangular strip of length 16 was cut into two strips of lengths 9 and 7. These two strips were placed on the table as shown in the figure.

It is known that the area of the part of the table covered only by the left strip is 27, and the area of the part of the table covered only by the right strip is 18. Find the area of the part of the table covered by both strips.

![](https://cdn.mathpix.com/cropped/2024_05_06_d55ea3e8288d58a3f771g-21.jpg?height=579&width=747&top_left_y=90&top_left_x=351)
Answer: 13.5.

Solution. Since the width of the two resulting strips is the same, their areas are in the ratio of their lengths, i.e., $9: 7$. Let $S$ be the area covered by both strips. Then $\frac{27+S}{18+S}=\frac{9}{7}$, from which we get $7 \cdot(27+S)=9 \cdot(18+S)$. Solving this linear equation, we get $S=13.5$.