Okay so I am working on this problem:

Solve $\displaystyle xu_t + uu_x = 0$ with $\displaystyle u(x, 0) = x.$(Hint: Change variables $\displaystyle x \rightarrow x^2$.)

However, I am not sure how to use the change of variables hint that is given or why it is needed. My thinking is that I could just use the method of characteristic as normal to get the solution. Any help is appreciated.