Question

How many liters each of a 55% acid solution and a 75% acid solution must be used to produce 40 liters of a 65% acid solution?

Answer 1

To prepare 40 liters of a 65% acid solution, 20 liters of a 55% acid solution and 20 liters of a 75% acid solution are needed, as derived from solving a system of equations based on volume and concentration.

Step-by-step explanation:

To determine the answer to the question of how many liters each of a 55% acid solution and a 75% acid solution must be used to produce 40 liters of a 65% acid solution, we can set up a system of equations based on the principle of mass conservation for the acid.

Let x be the volume of the 55% solution and y be the volume of the 75% solution. The total volume of the final solution is given as 40 liters.

The first equation represents the total volume:

• x + y = 40

The second equation represents the total amount of pure acid:

• 0.55x + 0.75y = 0.65 × 40

Solving the system of equations:

1. Substitute y from the first equation into the second equation: 0.55x + 0.75(40 - x) = 26
2. Solve for x: 0.55x + 30 - 0.75x = 26, which simplifies to -0.20x = -4, so x = 20 liters
3. Substitute x into y = 40 - x to get y = 20 liters

Therefore, 20 liters of the 55% solution and 20 liters of the 75% solution are required.