A pharmacist needs 20 liters of a 2% saline solution. She has a 1% solution and a 5% solution available. How many liters of the 1% solution and how many liters of the 5% solution should she mix to make the 2% solution?

15 liters of 1% solution and 5 liters of 5% solution

Step-by-step explanation:

Let x liters of 1% solution needed and y liters of 5% solution needed to make this mixture.

We can say:

20 (0.02) = x (0.01) + y (0.05)

0.4 = 0.01x + 0.05y

Also, we can write:

x + y = 20

x = 20 - y

We can put this into equation 1:

0.4 = 0.01x + 0.05y

0.4 = 0.01 (20 - y) + 0.05y

0.4 = 0.2 - 0.01y + 0.05y

0.2 = 0.04y

y = 5 liters

Hence, x = 20 - 5 = 15 liters

We need,

15 liters of 1% solution and 5 liters of 5% solution