All GRE Math Resources
Example Question #1 : Proportion / Ratio / Rate
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?
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?
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 #3 : 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?
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 :