Final answer:
To find out how much of the 30% acid and 65% acid solutions are needed to make 14 liters of a 40% acid solution, solve the system of equations derived from the mixture's requirements.
Step-by-step explanation:
The student is looking to make 14 liters of a 40% acid solution using solutions with concentrations of 30% acid and 65% acid. Let's call the amount of the 30% solution needed x liters, and the amount of the 65% solution needed y liters. We are trying to solve the following system of equations:
- 30% of x + 65% of y = 40% of 14
- x + y = 14
To solve for x and y, we need to strategically manipulate and combine these equations. By converting percentages to decimals, the equations become:
- 0.30x + 0.65y = 0.40 * 14
- x + y = 14
Solving the system of equations will give us the exact amount of each solution needed to make the desired acid mixture.