Question

a 5-gallon mixture contains 40% acid. A 3-gallon mixture contains 50% acid. what percent acid is obtained by putting the two mixtures together? show your work.

Answer 1

so the 5 gallons ones is 40% acid, how much acid solute is in it anyway? well just 40% of 5 or namely 0.4*5 = 2 gallons.

the 3 gallons one is 50%, likewise it has 0.50 * 3 = 1.5 gallons of acid solute in it.

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{1st mixture}&5&0.4&\stackrel{(5)(0.4)}{2}\\ \textit{2nd mixture}&3&0.5&\stackrel{(3)(0.5)}{1.5}\\ \cline{2-4}&\\ mixed&8&p&3.5 \end{array} \\\\\\ 8p=3.5\implies p=\cfrac{3.5}{8}\implies p=0.4375\implies p=\stackrel{\%}{43.75}$