A rectangular grassy park has an area of $4000 \mathrm{~m}^{2}$. In the park, two concrete paths cross each other, running parallel to the sides. The area of one path is $400 \mathrm{~m}^{2}$, and the other is $250 \mathrm{~m}^{2}$. What percentage of the park's area is covered by grass?
Let the lengths of the adjacent sides of the park be $a$ and $b$, and the widths of the concrete paths be $x$ and $y$. The area of the park and the paths are given by:

$$
\begin{aligned}
& a b=400 \mathrm{~m}^{2} \\
& a y=400 \mathrm{~m}^{2} \\
& b x=250 \mathrm{~m}^{2}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_05_02_cc3c8fb53818d634b7e2g-1.jpg?height=271&width=509&top_left_y=529&top_left_x=797)

From the system of equations, it follows that $x y=25 \mathrm{~m}^{2}$. The total area of the two concrete paths includes this $25 \mathrm{~m}^{2}$ twice, so the actual area of the concrete is

$$
400+250-25=625 \mathrm{~m}^{2}
$$

The area of the grassy part is $3375 \mathrm{~m}^{2}$; this is $\frac{3375}{4000} \cdot 100 \%=84.375 \%$ of the park's area.

Zoltán Gonda (Budapest, Kilián Gy. Secondary School, 4th grade)