Nurse erika needs to prepare 12 liters of a 10% saline solution. The stockroom only has 7 % and 15% saline solutions. How much of each solution should erika mix together to get 12 litres of a 10% saline solution
let amount of 7% solution be x L
then the amount of 15% solution must be 12-x L
.07x + .15(12-x) = .10(12)
times 100
7x + 15(12-x) = 120
7x + 180 - 15x = 120
-8x = -60
x = 7.5
She should use 7.5 L of the 7% and 4.5 of the 15% solution
check:
.07(7.5) + .15(4.5)
= 1.2
and 10% of 12 L is 1.2
To determine the amounts of the 7% and 15% saline solutions that Nurse Erika needs to mix, we can set up an equation based on the principle of concentration:
Let's assume Nurse Erika needs to mix x liters of the 7% saline solution and (12 - x) liters of the 15% saline solution.
The total amount of saline in the mixture will be the sum of the saline amounts from the two solutions. For the 7% saline solution, the amount of saline is 0.07x liters, and for the 15% saline solution, the amount of saline is 0.15(12 - x) liters.
Next, we set up the equation:
0.07x + 0.15(12 - x) = 0.10(12)
Simplifying the equation:
0.07x + 1.8 - 0.15x = 1.2
Combining like terms:
-0.08x + 1.8 = 1.2
Subtracting 1.8 from both sides:
-0.08x = -0.6
Dividing by -0.08:
x = 7.5
Therefore, Nurse Erika needs to mix 7.5 liters of the 7% saline solution with (12 - 7.5) = 4.5 liters of the 15% saline solution to obtain 12 liters of a 10% saline solution.