Final answer:
To find the appropriate volumes of 55% and 75% acid solutions needed to create a 65% acid solution, a system of linear equations must be solved, which aligns with the subject of mathematics at the high school level.
Step-by-step explanation:
The question involves a system of linear equations which is a concept within algebra, a branch of mathematics. To determine how many liters of a 55% acid solution and a 75% acid solution are needed to create 40 liters of a 65% acid solution, we can set up two equations based on the principles of concentration and volume. Let's denote the volume of the 55% solution as x liters and the volume of the 75% solution as y liters.
The first equation represents the total volume of the mixture: x + y = 40. The second equation relates to the amount of acid in the final solution: 0.55x + 0.75y = 0.65 × 40. Solving this system of equations, we can find the values of x and y that satisfy both equations. Once we have the solution to the system, we round off to two decimal places if needed to find the exact volume required for each solution.