Step 1 :Let's denote the amount of the 40% solution as x and the amount of the 90% solution as y.
Step 2 :We know that the total volume of the solution must be 250 mL, so we can write the equation as \(x + y = 250\).
Step 3 :The total amount of alcohol in the solution must be 45% of the total volume, so we can write the equation as \(0.4x + 0.9y = 112.5\).
Step 4 :Solving this system of equations, we find that \(x = 225\) and \(y = 25\).
Step 5 :Final Answer: You will need \(\boxed{225 \mathrm{~mL}}\) of the 40% solution and \(\boxed{25 \mathrm{~mL}}\) of the 90% solution.