Question

HELP!!!!! VERY LOST!!!!!

Work attached.

Answer 1

`x=\textit{oz of solution at 10\%}\\\\ ~~~~~~ 10\%~of~x\implies \cfrac{10}{100}(x)\implies 0.1 (x) \\\\\\ y=\textit{oz of solution at 20\%}\\\\ ~~~~~~ 20\%~of~y\implies \cfrac{20}{100}(y)\implies 0.2 (y) \\\\\\ \textit{32 oz of solution at 12\%}\\\\ ~~~~~~ 12\%~of~32\implies \cfrac{12}{100}(32)\implies 0.12 (32)\implies 3.84 \\\\[-0.35em] ~\dotfill`

`\begin{array}{lcccl} &\stackrel{oz}{amount}&\stackrel{\textit{\% of oz that is}}{\textit{salt only}}&\stackrel{\textit{oz of}}{\textit{salt only}}\\ \cline{2-4}&\\ \textit{10\% salt water}&x&0.10&0.1x\\ \textit{20\% salt water}&y&0.20&0.2y\\ \cline{2-4}&\\ mixture&32&0.12&3.84 \end{array}~\hfill \begin{cases} x + y = 32\\\\ 0.1x+0.2y=3.84 \end{cases} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{using the 1st equation}}{x+y=32}\implies y=32-x \\\\\\ \stackrel{\textit{using the 2nd equation}}{0.1x+0.2y=3.84}\implies \stackrel{\textit{substituting from the 1st equation}}{0.1x+0.2(32-x)~~ = ~~3.84} \\\\\\ 0.1x+6.4-0.2x=3.84\implies 6.4-0.1x=3.84\implies 6.4=0.1x+3.84 \\\\\\ 2.56=0.1x\implies \cfrac{2.56}{0.1}=x\implies \boxed{25.6=x}\hspace{5em}\stackrel{ 32~~ - ~~25.6 }{\boxed{y=6.4}}`