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Example Questions
Example Question #81 : Fractions
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 #1 : 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
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?
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 :
All GRE Math Resources
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