Final answer:
The quantities of the unknowns when mixing a 50% salt solution with a 10% salt solution to make a 25% solution should be thought of as variables, which can be determined using algebra and the formula C1V1 = C2V2.
Step-by-step explanation:
Mixing Salt Solutions Problem
When you are mixing a 50% salt solution with a 10% salt solution to make 30 liters of a 25% solution, the best way to think about the quantities of the unkowns is as variables. This is because the amounts of each solution required to achieve the 25% concentration are not fixed and need to be calculated. In these kinds of problems, we typically use the concept of concentrations and volumes, known from chemistry, and apply mathematical methods like algebra to find the unknown volumes of each starting solution.
We can apply the formula C1V1 = C2V2 (where C1 and V1 are the concentration and volume of the first solution, and C2 and V2 are the concentration and volume of the final solution) to ensure the total amount of solute remains constant after dilution. This formula can be used twice: once for the 50% solution and once for the 10% solution.
In the mathematical representation, the amount of solute in the final solution must be equal to the combined amount of solute from both the 50% solution and the 10% solution. Setting up a system of equations with these conditions will help us find the volumes of each starting solution needed.