A surgeon needs 9 liters of a 3% saline solution. She has a 1% solution and a 10% solution available. How many liters of the 1% solution and how many liters of the 10% solution should she mix to make the 3% solution?

7 L of the 1% solution and 2 L of the 10% solution should she mix to make the 9 L of 3% solution.

Explanation:

Let the volume of 1% solution be mixed to make 3% solution = a L

Let the volume of 10% solution be mixed to make 3% solution = b L

Given, Volume of 3% solution = 9 L

Thus, a + b = 9 ... 1

Also,

Applying C₁V₁ + C₂V₂ = C₃V₃

Where,

C₁ is the concentration of the 1% liquid

C₂ is the concentration of the 10% liquid

C₃ is the concentration of the 3% liquid

V₁ is the volume of the 1% liquid (a L)

V₂ is the volume of the 10% liquid (b L)

V₃ is the volume of the 3% liquid (9 L)

So,

1*a + 10*b = 9*3

a + 10b = 27 ... 2

Solving equation 1 and 2, we get:

a = 7 L and b = 2 L

Thus, 7 L of the 1% solution and 2 L of the 10% solution should she mix to make the 3% solution.

7 L of the 1% solution

2 L of the 10% solution