Question

A 5-gallon jug of cleaning solution contains 6% bleach. How much pure water should be added to it to dilute to 4% bleach?

Answer 1

Let's bear in mind that 5 gallons with a solution of 6% bleach, contains some water plus some bleach, how much bleach?  well, is just 6% of 5 gallons or namely (6/100) * 5 gallons, or 0.30 gallons.

if we use "x" gallons of water, well pure water has no bleach, so is 0% bleach, and it has a (0/100) * x or 0x gallons of bleach.

the mixture will be say "y" gallons, and is 4% bleach, so (4/100) * y is 0.04y gallons in the mixture of bleach.

$\bf \begin{array}{lcccl} &\stackrel{gallons}{quantity}&\stackrel{\textit{\% of bleach}}{amount}&\stackrel{\textit{gallons of bleach}}{amount}\\ &------&------&------\\ \textit{pure water}&x&0.00&0x\\ \textit{6\% solution}&5&0.06&0.3\\ -----&------&------&------\\ mixture&y&0.04&0.04y \end{array} \\\\\\ \begin{cases} x+5=\boxed{y}\\ 0x+0.3=0.04y\\ ---------\\ 0.3=0.04\left( \boxed{x+5} \right) \end{cases} \\\\\\ 0.3=0.04x+0.2\implies 0.1=0.04x\implies \cfrac{0.1}{0.04}=x\implies 2.5=x$