Question 679432
The solution she has in the bucket has 80% water (as you found out), including 14.4 fl oz. water in a total of 18 fl oz. solution.
Barbara will need to add ammonia, but only after removing some ({{{x}}} fl oz.) of the solution she has in the bucket.
If Barbara wants an 18 fl oz. bucket full of 25% ammonia, she will need to have in that bucket
{{{18*0.25=4.5}}} fl oz. ammonia (25% ammonia) and
{{{18*0.75=13.5}}} fl oz. water (75% water).
Barbara will have to start by removing some of that 80% water solution to end up with just 13.5 fl oz. water in the bucket.
Removing {{{x}}} fl oz. of solution, gets rid of {{{0.8x}}} fl oz. of water,
leaving {{{14.4-0.8x}}} fl oz. of water.
Since the amount of water needed is {{{13.5}}} fl oz., our equation is
{{{highlight(13.5=14.4-0.8x)}}}
{{{13.5=14.4-0.8x}}} --> {{{0.8x=14.4-13.5}}} --> {{{0.8x=0.9}}} --> {{{x=0.9/0.8}}} --> {{{highlight(x=1.125)}}} fl oz.