so hmmm 7% of anything is (7/100) * anything.
now... how much iodine is in the 20oz solution? well (7/100) * 20, or 1.4 is iodine, the rest is some other substances, but 1.4oz is iodine.
now, he wants to drop it to a mixture of 4% iodine, let's say the mixture "m" in ounces, has 4% iodine, how much is that? well (4/100) * m, or 0.04m.
well, he wants to do so by adding say "a" oz of pure alcohol... how much iodine in the alcohol? none or 0%, or (0/100) * a, or 0.00a or just 0a or 0 anyway.
[tex]\bf \begin{array}{lccclll}
&\stackrel{oz}{amount}&\stackrel{iodine~\%}{quantity}&\stackrel{iodine~oz}{quantity}\\
&------&------&------\\
\textit{20oz sol'n}&20&0.07&1.4\\
\textit{pure alcohol}&a&0.00&0a\\
------&------&------&------\\
mixture&m&0.04&0.04m
\end{array}[/tex]
now, whatever "m" may be, we know that 20 + a = m, and we also know likewise that 1.4+0 = 0.04m.
[tex]\bf \begin{cases}
20+a=\boxed{m}\\
1.4+0=0.04m\\
----------\\
1.4=0.04\left( \boxed{20+a} \right)
\end{cases}
\\\\\\
1.4=0.04a+0.8\implies 1.4-0.8=0.04a\implies 0.6=0.04a
\\\\\\
\cfrac{0.6}{0.04}=a\implies \stackrel{oz}{15}=a[/tex]
