Question

Can anyone explain? Thanks!

Answer 1

$\bf \stackrel{\textit{quotient of \underline{a} and \underline{c} is 8}}{\cfrac{a}{c}=8}~\hspace{3em}\stackrel{\textit{product of \underline{a} and \underline{c} is 2}}{ac=2}~\hspace{3em}\stackrel{\textit{quotient of \underline{a} and \underline{b} is -16}}{\cfrac{a}{b}=-16} \\\\\\ \stackrel{\textit{product of \underline{a} and \underline{b} is -1}}{ab=-1}~\hspace{3em}\stackrel{\textit{quotient of \underline{b} and \underline{c} is 8}}{\cfrac{b}{c}=-0.5} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ac=2\implies a=\cfrac{2}{c}~\hspace{7em} therefore\qquad \cfrac{a}{c}=8\implies \cfrac{~~\frac{2}{c}~~}{c}=8 \\\\\\ \cfrac{2}{c}\cdot \cfrac{1}{c}=8\implies \cfrac{2}{c^2}=8\implies \cfrac{2}{8}=c^2\implies \cfrac{1}{4}=c^2\implies \sqrt{\cfrac{1}{4}}=c \\\\\\ \cfrac{\sqrt{1}}{\sqrt{4}}=c\implies \boxed{\cfrac{1}{2}=c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ac=2\implies a\cdot \cfrac{1}{2}=2\implies \boxed{a=4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ab=-1\implies 4b=-1\implies \boxed{b=-\cfrac{1}{4}}$

and you can check those values in those equations.