Question

John is preparing 50 liters of a 25% saline solution. He only has 40% and a 10% solution in his lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?

Answer 1

To make a 25% saline solution, John should mix equal amounts of the 40% and 10% solutions. Therefore, he should mix 25 liters of each solution to obtain a 50-liter solution.

Step-by-step explanation:

John has to combine some of the 40% and 10% solutions to make a 25% saline solution. Assume that x litres of the 40% solution and y litres of the 10% solution need to be combined. The mixture will have a total volume of x + y litres.

The 40% solution contains 0.4x litres of salt (40% of x litres), while the 10% solution contains 0.1y litres of salt (10% of y litres).

The amount of salt in the combination should be 0.25 times the total volume for a 25% saline solution. Hence, 0.25(x + y) = 0.4x + 0.1y.

This equation can be simplified to 0.15x = 0.15y to solve. Consequently, x = y.

This means that John should mix equal amounts of the 40% and 10% solutions. In this case, he should mix 25 liters of the 40% solution and 25 liters of the 10% solution to obtain 50 liters of a 25% saline solution.