1953 AHSME Problems/Problem 9
Problem
The number of ounces of water needed to reduce ounces of shaving lotion containing
% alcohol to a lotion containing
% alcohol is:
Solution
Say we add ounces of water to the shaving lotion. Since half of a
ounce bottle of shaving lotion is alcohol, we know that we have
ounces of alcohol. We want
(because we want the amount of alcohol,
, to be
, or
, of the total amount of shaving lotion,
). Solving, we find that
So, the total amount of water we need to add is
.