How many liters each of a $35 \%$ acid solution and a $85 \%$ acid solution must be used to produce 50 liters of a $55 \%$ acid solution? (Round to two decimal places if necessary.) Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts liters of $35 \%$ acid solution liters of $85 \%$ acid solution

Step 1 ：Define two variables, x and y, to represent the liters of $35 \%$ acid solution and $85 \%$ acid solution respectively.

Step 2 ：Set up the system of equations based on the problem. The first equation is based on the total volume of the solution, which is 50 liters. So, \(x + y = 50\). The second equation is based on the percentage of acid in the solution. So, \(0.35x + 0.85y = 0.55 \times 50\).

Step 3 ：Solve the system of equations to find the values of x and y.

Step 4 ：The solution to the system of equations is \(x = 30\) and \(y = 20\).

Step 5 ：This means that we need to mix \(\boxed{30}\) liters of the $35 \%$ acid solution and \(\boxed{20}\) liters of the $85 \%$ acid solution to produce 50 liters of a $55 \%$ acid solution.