Question

A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 45% and the third contains 75%. He wants to use all three solutions to obtain a mixture of 156 liters containing 35% acid, using 2 times as much of the 75% solution as the 45% solution. How many liters of each solution should be used?

Answer 1

To obtain a mixture of 156 liters containing 35% acid, the chemist should use 78 liters of the 25% acid solution, 156 liters of the 45% acid solution, and 78 liters of the 75% acid solution.

Step-by-step explanation:

To solve this problem, we can set up a system of equations representing the amounts of each acid solution used in the mixture.

Let's say the amount of the first acid solution used is x liters.

The amount of the second acid solution used would be 2x liters since we are using twice as much of the 75% solution as the 45% solution.

Therefore, the amount of the third acid solution used would be 156 - x - 2x = 156 - 3x liters.

We can now set up an equation using the percentages of acid in each solution:

(0.25x + 0.45(2x) + 0.75(156 - 3x)) / 156 = 0.35

Simplifying the equation and solving for x, we can determine the amount of each solution:

x = 78 liters of the 25% acid solution

2x = 156 liters of the 45% acid solution

156 - 3x = 78 liters of the 75% acid solution