Question

Calculate the percentage of alcohol in a lotion containing 2liters of which hazel (14% of alcohol), 1liter of alcohol (95%) and enough boric acid solution to make 5liters

Answer 1

from the reading above, doesn't seem the boric acid has any alcohol at all, so we can say 0% alcohol.

now let's see how many liters we have hmmm 2 of hazel, 1 of alcohol and the rest in boric acid, to make a total of 5 liters, so boric acid must be 2, since 2 + 1 + 2 = 5.

how much alcohol is there in 14% of 2 liters?

`\begin{array}ll \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{14\% of 2}}{\left( \cfrac{14}{100} \right)2}\implies 0.28`

how much alcohol is there in 95% of 1? well, no to bore you to death, is just 0.95 liters, and we know the boric acid has no alcohol.

so in the 5 liters of the lotion, we have 0.28 liters plus 0.95 liters of alcohol total, that's 1.23 liters total.

now, if we know the 100% of the lotion is the 5 liters, how much is 1.23 liters off of it in percentage?

`\begin{array}{ccll} liters&\%\\ \cline{1-2} 5 & 100\\ 1.23& x \end{array} \implies \cfrac{5}{1.23}~~=~~\cfrac{100}{x} \\\\\\ 5x=123\implies x=\cfrac{123}{5}\implies x=\stackrel{\%}{24.6}`