Question

how many liters of 15% acid and 33% acid should be mixed to get 120 liter of 21% acid? what's the equation for this?

Answer 1

$\bf \begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of acid}}{amount}&\stackrel{\textit{liters of acid}}{amount}\\ &------&------&------\\ \textit{15\% acid}&x&0.15&0.15x\\ \textit{33\% acid}&y&0.33&0.33y\\ -----&------&------&------\\ mixture&120&0.21&25.2 \end{array}$

$\bf \begin{cases} x+y=120\implies \boxed{y}=120-x\\ 0.15x+0.33y=25.2\\ --------------\\ 0.15x+0.33\left( \boxed{120-x} \right)=25.2 \end{cases} \\\\\\ 0.15x-0.33+39.6=25.2\implies -0.18x=-14.4 \\\\\\ x=\cfrac{-14.4}{-0.18}\implies x=80$

how many liters will it be of the 33% acid?  well, y = 120 - x.