Tom has 1 cup of a 5% vinegar-water solution, 2 cups of a 10% vinegar-water solution, and 3 cups of a 15% vinegar-water solution. He needs at least 8 cups of a 5% vinegar-water solution for his chemistry project. What is the number of cups of pure water he should add to the total of all his vinegar-water solutions to complete the project?

Another eight cups of pure water will be required.

Explanation:

Start by calculating the amount (in cups) of vinegar in these six cups:

Therefore, if these six cups of solutions were mixed, the mixture would contain cups of vinegar. Also, the mixture is supposed to have a volume of six cups. Therefore, the concentration of this six-cup mixture would be:

.

In other words, if these six cups of vinegar-water solutions are mixed, it would be necessary to dilute (by adding more water) before reaching the concentration of .

The goal is to dilute this solution with cups of vinegar to a concentration of . Consider: what would be the volume the solution after dilution?

The volume of a solution can be found from the quantity and concentration of its solute:

After dilution, the volume of this solution would be:

.

At this moment, this solution only has a volume of six cups. Therefore, cups of pure water will be required.

some of the qualities most frequently associated with the baroque are grandeur, sensuous richness, drama, vitality, movement, tension, emotional exuberance, and a tendency to blur distinctions between the various arts.

solute : a solute is a substance that is dissolved in another substance is known as a solvent. it is mixed with a special mixture know as homogeneous mixture.

solvent: a solvent is a substance that dissolved a solute, which results in a solution is known as solvent.