Question

a chemist has one solution that is 60% acid into second does 40% acid how many gallons of each should be mixed together to get 200 gallons of a solution that is 55% acid

Answer 1

keeping in mind that

`\bf \begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}`

so if the amount of the 60% solution is "x" gallons, then the acid in it is 0.6x, and likewise the 40% solution has 0.4y gallons.

`\bf \begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{60\% sol'n}&x&0.6&0.6x\\ \textit{40\% sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&200&0.55&110 \end{array}`

`\bf \begin{cases} x+y=200\implies \boxed{y}=200-x\\\\ 0.6x+0.4y=110\\[-0.5em] \hrulefill\\ 0.6x+0.4\left( \boxed{200-x} \right)=110 \end{cases} \\\\\\ 0.6x-0.4x+80=110\implies 0.2x=30\implies x=\cfrac{30}{0.2}\implies \blacktriangleright x=150 \blacktriangleleft \\\\\\ y=200-x\implies \blacktriangleright y=50 \blacktriangleleft`