You need a 20\% alcohol solution. On hand, you have a $385\mathrm{mL}$ of a $15\mathrm{\%}$ alcohol mixture. You also have $75\mathrm{\%}$ alcohol mixture. How much of the $75\mathrm{\%}$ mixture will you need to add to obtain the desired solution?
You will need
$\mathrm{mL}$ of the $75\mathrm{\%}$ 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 $\boxed{{\displaystyle 35}}$ mL of the 75% solution.