Step 1 :Let's denote the volume of water to be added as \(W\) (in gallons), and the volume of premium antifreeze solution to be added as \(P\) (in gallons).
Step 2 :From the problem, we know that the total volume of the mixture should be 170 gallons, so we have the equation \(W + P = 170\).
Step 3 :We also know that the mixture should be 80% pure antifreeze. Since water doesn't contain any antifreeze and the premium solution is 85% antifreeze, we have the equation \(0*W + 0.85*P = 0.8*170\).
Step 4 :We can solve this system of equations to find the values of \(W\) and \(P\).
Step 5 :The solution to the system of equations is \(P = 160\) and \(W = 10\).
Step 6 :This means that to obtain 170 gallons of a mixture that contains 80% pure antifreeze, the company must mix 10 gallons of water with 160 gallons of the premium antifreeze solution.
Step 7 :Final Answer: The company must mix \(\boxed{10}\) gallons of water with \(\boxed{160}\) gallons of the premium antifreeze solution.