Question

How many liters each of a 20 % acid solution and a 45 % acid solution must be used to produce 50 liters of a 25 % acid solution? (Round to two decimal places if necessary.) AnswerHow to enter your answer (opens in new window) 2 Points liters of 20 % acid solution. liters of 45 % acid solution: Keypac Keyboard Shortcu​

Answer 1

To produce 50 liters of a 25% acid solution, you need 40 liters of a 20% acid solution and 10 liters of a 45% acid solution.

Let x be the volume of the 20% acid solution and y be the volume of the 45% acid solution to make a total of 50 liters of a 25% acid solution.

We can set up a system of equations based on the given information:

1. The total volume equation:

x + y = 50

2. The acid content equation:

0.20x + 0.45y = 0.25 \times 50

Now, solve this system of equations to find x and y .

From the first equation, we can express x in terms of y :

x = 50 - y

Substitute this into the second equation:

0.20(50 - y) + 0.45y = 12.5

Solve for y :

10 - 0.20y + 0.45y = 12.5

0.25y = 2.5

y = 10

Now, substitute y = 10 back into the first equation to find x :

x + 10 = 50

x = 40

Therefore, you need 40 liters of the 20% acid solution and 10 liters of the 45% acid solution to produce 50 liters of a 25% acid solution.