If 𝑚m is increased by 15% and 𝑛n is decreased by 15%, the resulting numbers will be equal. What is the ratio of 𝑚m to 𝑛n?

Let's solve this step by step:

1. If m is increased by 15%, the resulting number will be 1.15m.
2. If n is decreased by 15%, the resulting number will be 0.85n.
3. According to the problem, these two resulting numbers are equal. So, we can set up the equation 1.15m = 0.85n.
4. To find the ratio of m to n, we need to isolate m/n. We can do this by dividing both sides of the equation by 1.15n. This gives us m/n = 0.85/1.15.
5. Simplifying the right side of the equation gives us the ratio of m to n, which is approximately 0.7391.

So, the ratio of m to n is approximately 0.7391.