You need a 20\% alcohol solution. On hand, you have a $385 \mathrm{~mL}$ of a $15 \%$ alcohol mixture. You also have $75 \%$ alcohol mixture. How much of the $75 \%$ mixture will you need to add to obtain the desired solution? You will need $\mathrm{mL}$ of the $75 \%$ solution

Step 1 ：We are given a 385 mL of a 15% alcohol mixture and we want to add some amount of a 75% alcohol mixture to it to obtain a 20% alcohol solution. Let's denote the amount of the 75% solution we need to add as x mL.

Step 2 ：The total volume of the final solution will be 385 + x mL, and it will contain 20% alcohol.

Step 3 ：The 385 mL of 15% solution contains \(0.15 \times 385 = 57.75\) mL of alcohol.

Step 4 ：The x mL of 75% solution contains \(0.75x\) mL of alcohol.

Step 5 ：The amount of alcohol in the final solution is equal to the sum of the amount of alcohol in the initial solutions. So, we can set up the following equation: \(0.20 \times (385 + x) = 57.75 + 0.75x\).

Step 6 ：Solving this equation gives us the value of x.

Step 7 ：Final Answer: You will need \(\boxed{35}\) mL of the 75% solution.