<s>[INST] A container contains a certain number of balls, each of which is either colored either white, black or red. We are given the following information:
- For every 5 white balls, exactly 2 black balls are present.
- For every 3 black balls, exactly 1 red ball is present.
From this information, can we determine the number of red balls, \(r\), solely based on the number of white balls, \(w\)? If yes, explain how. If no, provide a valid counter-example.[/INST]