In a distribution, a score of x=60 has a z-score of -3.0.. a score of x=85 has a z-score of 2.0. what are the mean and standard deviation for this population?

The formula for a z-score is

We don't have μ, the mean, or σ, the standard deviation.  We can, however, set up a system of two equations with the information we do have.  We know:

We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation.  We do this by multiplying the bottom of each equation by σ:

Now we'll get the variables on the same side of the equation.  We'll do this by adding μ to both sides:

Now we'll write this vertically:

We will "eliminate" μ by subtracting the bottom equation:

Divide both sides by -5:

Our standard deviation is 5.  Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.