3. Coaches Ivan and Marko are organizing a treasure hunt through two forest trails. Katja walked both trails, Ivan's and Marko's, and took a total of 2024 steps of the same length. If she had taken 204 fewer steps on Ivan's trail and 24 more steps on Marko's trail, she would have taken the same number of steps on both trails. How many steps did Katja take on Ivan's trail, and how many on Marko's trail?
First solution.

Let's illustrate the relationship between Mark's and Ivan's paths with a diagram. When we reduce Ivan's path by 204 steps and increase Mark's path by 24 steps, we get the same length, which we can represent as follows:

![](https://cdn.mathpix.com/cropped/2024_05_30_0b00c6f52e60bdba44a4g-02.jpg?height=326&width=1585&top_left_y=1713&top_left_x=241)

Since Mark's and Ivan's paths together are as long as 2024 of Katja's steps, and we can see from the previous image that they differ by 228 steps, we can represent this as follows:

![](https://cdn.mathpix.com/cropped/2024_05_30_0b00c6f52e60bdba44a4g-02.jpg?height=280&width=1385&top_left_y=2167&top_left_x=244)

Katja made (2024 - 228) : $2=898$ steps on Mark's path.

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