Answer:
We need 5.7 liters of the 5% volume solution and 4.3 liters of the 40% volume solution.
Step-by-step explanation:
Let V₁ be the volume of the 5% solution required and V₂ be the volume of 40% solution required.
Since mass = concentration × volume, the combined mass of the 5% and 40% volume solution equal the mass of the 10 liter 20% volume solution.
So, 0.05V₁ + 0.4V₂ = 0.2 × 10
0.05V₁ + 0.4V₂ = 2 (1)
Also, the total volume of the solution must equal 10 liters. So,
V₁ + V₂ = 10 (2)
V₁ = 10 - V₂ (3)
substituting (3) into (1), we have
0.05(10 - V₂) + 0.4V₂ = 2
0.5 - 0.05V₂ + 0.4V₂ = 2
collecting like terms, we have
- 0.05V₂ + 0.4V₂ = 2 - 0.5
0.35V₂ = 1.5
dividing through by 0.35, we have
V₂ = 1.5/0.35
V₂ = 4.29
V₂ = 4.3 liters to the nearest tenth of a liter
Substituting V₂ into (3), we have,
V₁ = 10 - 4.3
V₁ = 5.7 liters
So, we need 5.7 liters of the 5% volume solution and 4.3 liters of the 40% volume solution.
