Question

A pharmacist wants to mix a 27% saline solution with a 13% saline solution to get 112 mL of a 21% saline solution. How much of each solution should she

use? Round your answer to the nearest mL.

Answer 1

`x=\textit{mL of solution at 27\%}\\\\ ~~~~~~ 27\%~of~x\implies \cfrac{27}{100}(x)\implies 0.27 (x) \\\\\\ y=\textit{mL of solution at 13\%}\\\\ ~~~~~~ 13\%~of~y\implies \cfrac{13}{100}(y)\implies 0.13 (y) \\\\\\ \textit{112 mL of solution at 21\%}\\\\ ~~~~~~ 21\%~of~112\implies \cfrac{21}{100}(112)\implies 23.52 \\\\[-0.35em] ~\dotfill`

`\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{saline only}}&\stackrel{\textit{mL of}}{\textit{saline only}}\\ \cline{2-4}&\\ \textit{27\% Sol'n}&x&0.27&0.27x\\ \textit{13\% Sol'n}&y&0.13&0.13y\\ \cline{2-4}&\\ mixture&112&0.21&23.52 \end{array}~\hfill \begin{cases} x + y = 112\\\\ 0.27x+0.13y=23.52 \end{cases} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{using the 1st equation}}{x+y=112}\implies y=112-x \\\\\\ \stackrel{\textit{substituting`