Step 1 :The problem is asking for the amount of Demerol in milliliters that should be given to the client. To solve this, we need to set up a proportion to find out how many milliliters correspond to 75 milligrams of Demerol. The proportion is set up as follows: 120 milligrams is to 2 milliliters as 75 milligrams is to x milliliters.
Step 2 :Solving for x will give us the answer. We can set up the equation as follows: \(\frac{120}{2} = \frac{75}{x}\)
Step 3 :Cross multiplying gives us: \(120x = 150\)
Step 4 :Solving for x, we get: \(x = \frac{150}{120} = 1.25\)
Step 5 :Final Answer: The client should be given \(\boxed{1.25}\) milliliters of Demerol.