An alcohol solution consists of 6 gallons of pure water and x gallons of alcohol, x > 0. Let f(x) be the ratio of the volume of alcohol to the total volume of liquid. [Note that f(x) is the concentration of the alcohol in the solution.]
(a) Find a possible formula for f(x).
To find a formula for f(x), we need to determine the ratio of alcohol to the total volume of liquid in the solution.
In this case, the total volume of liquid is 6 gallons of pure water plus x gallons of alcohol, so it is 6 + x gallons.
The volume of alcohol in the solution is x gallons.
Therefore, the formula for f(x) can be given as:
f(x) = x / (6 + x)