transform z-scores to scale

Hello,

I was wondering if anyone could help with solving how z-scores (x-u/SD) have been converted into a scale with a set top score if you have the z score values and the rescaled values?

Is there a fomula to rearrange?

I posted this under stats as there is use of z-scores but apologies if it belongs elsewhere!

Thanks,

Would the rescaled values have the same z score as the original? Is the only way to do this kind of rescaling by adding or subtracting values from the raw z scores?