Question

A scientist needs to make 2 liters of saline solution (salt water), in which the salt level must be at 15% concentration (meaning 15% of the water is salt). Unfortunately, the scientist only has two types of saline solution in his possession. He has saline solution with a 10% concentration level and saline solution with a 35% concentration level.

Answer 1

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.

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.