If the lab technician needs 30 liters of a 25% acid solution, how many liters of the 10% and the 30% acid solutions should she mix to get what she needs?

7.5 liters of 10% solution and 22.5 liters of 30% solution

Step-by-step explanation:

Let there be x liters of 10% acid solution and y liters of 30% acid solution. Lab technician needs 30 liters of the final solution, so this means sum of x and y has to be 30 as these two will mix up to give the final acid solution. So, we can write the equation as:

x + y = 30

or

y = 30 - x

x liters of 10% solution and y liters of 30% solution will add up to give 30 liters of 25% acid solution. We can set up another equation as:

x liters of 10% acid + y liters of 30% acid = 30 liters of 25% acid

Changing percentage to decimals:

0.1 (x) + 0.3 (y) = 0.25 (30)

Using the value of y from our upper equation in the previous equation, we get:

0.1x + 0.3 (30-x) = 7.5

0.1x + 9 - 0.3x = 7.5

- 0.2x = - 1.5

x = 7.5 liters

y = 30 - x = 30 - 7.5 = 22.5 liters

This means, 7.5 liters of 10% acid solution and 22.5 liters of 30% acid solution would be needed to prepare 30 liters of 25% acid solution.