Question

A lab technician needs 25 liters of a solution that is a 15% acid concentration for a

certain experiment, but she only has a solution that is a 10% acid concentration and
a solution that is a 30% acid concentration.
a. Write a linear system to model this situation. Be sure to define your variables.
b. How many liters of the 10% concentration and 30% concentration will she
have to mix to get a 15% concentration?

Answer 1

To get a 15% concentration solution, the lab technician needs to mix a certain number of liters of 10% and 30% concentration solutions. We can set up a linear system to solve for those volumes.

Step-by-step explanation:

To find out how many liters of the 10% concentration and 30% concentration solutions the lab technician needs to mix to get a 15% concentration, we can set up a linear system.

Let x be the number of liters of the 10% concentration solution and y be the number of liters of the 30% concentration solution.

The total volume of the solution is 25 liters, so the first equation is: x + y = 25.

The acid concentration in the 10% solution is 0.10, and the acid concentration in the 30% solution is 0.30. The total acid in the solution is 0.15 * 25 = 3.75.

The second equation is: 0.10x + 0.30y = 3.75.

Solving this system of equations will give us the values of x and y, which are the number of liters of the 10% and 30% concentration solutions respectively.