Suppose a fuel mixture is 5% ethanol and 95% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new fuel mixture is 10% ethanol?
You need to add 0.0556 gallons of ethanol to the mixture.
You know that your mixture is 5% ethanol and 95% gasoline.
To determine how much ethanol you need to add to the 1-gallon sample in order to get the percent concetration of ethanol in the mixture to 10%, you first need to determine how much ethanol your sample currently has.
For a 1-gallon sample, you know that
Let's say that
This is equivalent to
So, if you add 0.0556 gallons of ethanol to the 1-gallon sample, you'll get a total mixture of 1.0556 gallons that is 10% ethanol.