Question

Allison needs 18 liters of a 5% 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 5% solution?

Answer 1

Answer:

10 liters of the 1% solution and 8 liters of the 10% solution she should mix to make the 5% solution.

Explanation:

Let the volume of 1% acid solution used to make the mixture = x L

So, the volume of 10% acid solution used to make the mixture = y L

Total volume of the mixture = x + y  = 18 L  .................. (1)

For 1% acid solution:

C₁ = 1% , V₁ = x L

For 10% acid solution :

C₂ = 10% , V₂ = y L

For the resultant solution of sulfuric acid:

C₃ = 5% , V₃ = 18 L

Using

C₁V₁ + C₂V₂ = C₃V₃

1×x + 10×y = 5×18

So,

x + 10y = 90  .................. (2)

Solving 1 and 2 we get,

x = 10 L

y = 8 L

Thus,

10 liters of the 1% solution and 8 liters of the 10% solution she should mix to make the 5% solution.