Z score

I'm having some trouble with my homework. The question is --

In a distribution with mean of 71 and a standard deviation of 18, there exists a score of 85. What is the equivalent score in a distribution with a mean of 50 and a standard deviation of 10?

My question is, are the z scores here gonna be the same? If so, then the z score is 0.78 and the equivalent score is 57.8
Please correct me if I'm wrong.