# GRE Math : How to find the volume of a solution

## Example Questions

### Example Question #1 : How To Find The Volume Of A Solution

A solution made up of  alcohol by volume is mixed with  liters of solution that is  alcohol by volume. How much, in liters, of the  alcoholic solution is needed to make a mixture that is  alcohol by volume?

Explanation:

Let  represent the number of liters of the 40% solution. Then it follows that  liters of the 40% solution plus 4 liters of the 10% solution will equal (x+4) liters of a 25% solution. This can be represented by the following equation:

Now solve for x:

You will need 4 liters of the 40% solution in order to make a mixture that is 25% alcohol by volume

### Example Question #2 : Proportion / Ratio / Rate

A solution is  parts water,  parts wine, and  part honey.  If a container of this solution contains  gallons of water, how much total solution is there in it?

gallons

gallons

gallons

gallons

gallons

gallons

Explanation:

To begin, notice that there is a  ratio between the water in your container and the water specified by the mix of the components.  Given that there are  total parts in your solution, this means that you can set up this equation:

Multiplying both sides by 8, you get:

There are  total gallons of solution.

### Example Question #1 : Proportion / Ratio / Rate

A solution is made up of  parts water,  parts orange juice, and  parts apple juice.  If you wanted the percentage of orange juice to be % of the solution, how many parts would you need to add?

Explanation:

To begin, you know that the basic form of the solution has a total of , or  parts.  Now, we know that we are going to have to add  parts of orange juice.  This means that the new solution will have  parts orange juice and  total parts (since we are adding to the original).  Since we want this to be % orange juice, we really want the following equation to be true:

Solve the following equation, therefore:

Multipy by :

Now, isolate :

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