Answer:
We need 1.6 liters of the 10 % concentration level and saline solution and 0.4 liters of the 35 % concentration level and saline solution.
Step-by-step explanation:
Let V₁ be the volume of the 10% concentration saline solution required and V₂ be the volume of 35% concentration saline solution required.
Since mass = concentration × volume, the total mass of the 10% and 35% volume saline solution equal the mass of the 2 liter 15% volume solution.
So, 0.1V₁ + 0.35V₂ = 2 × 0.15
0.1V₁ + 0.35V₂ = 0.3 (1)
Also, the total volume of the 15 % solution must equal 2 liters. So,
V₁ + V₂ = 2 (2)
V₁ = 2 - V₂ (3)
putting equation (3) into equation (1), we have
0.1(2 - V₂) + 0.35V₂ = 0.3
0.2 - 0.1V₂ + 0.35V₂ = 0.3
we now collect terms, so
- 0.1V₂ + 0.35V₂ = 0.3 - 0.2
0.25V₂ = 0.1
we now divide through by 0.25, so
V₂ = 0.1/0.25
V₂ = 0.4 liters
we now put V₂ into (3), we have,
V₁ = 2 - 0.4
V₁ = 1.6 liters
So, we need 1.6 liters of the 10 % concentration level and saline solution and 0.4 liters of the 35 % concentration level and saline solution.
