Theresa Morgan, a chemist, has a $15 \%$ hydrochloric achsolution and a $50 \%$ hydrochloric acid solution. How many liters of each should she mix to get 1028.125 liters of a hydrochloric acid solution with a $42 \%$ acid concentration? liters of $15 \%$ hydrochloric acid solution . liters of $50 \%$ hydrochloric acid solution . Submit Question Jump to Answer

Step 1 ：Let's denote the volume of the 15% solution as \(x\) and the volume of the 50% solution as \(y\).

Step 2 ：We can write down the following equations based on the problem:

Step 3 ：1) The total volume of the solution is 1028.125 liters: \(x + y = 1028.125\)

Step 4 ：2) The total amount of hydrochloric acid in the solution is 42% of the total volume: \(0.15x + 0.5y = 0.42 * 1028.125\)

Step 5 ：Solving this system of equations, we find that \(x = 235\) and \(y = 793.125\).

Step 6 ：Final Answer: Theresa Morgan should mix \(\boxed{235}\) liters of 15% hydrochloric acid solution and \(\boxed{793.125}\) liters of 50% hydrochloric acid solution to get 1028.125 liters of a hydrochloric acid solution with a 42% acid concentration.