Question

If x varies inversely with y and x = 6 when y = 10, find y when x = 8.

Answer 1

So x varies inversely to y

x=k/y

Answer 2

\(\bf \begin{array}{llll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{(\textit{some value })}{\textit{something else}}\\ \quad \\
y&=\cfrac{(n)}{x}
\end{array}\\ \quad \\
\textit{when x = 6, y = 10, thus }x=6\qquad y=10\implies y=\cfrac{{\color{red}{ n}}}{x}\implies 10=\cfrac{{\color{red}{ n}}}{6}\)

solve for "n" to find "n" or the "variation constant"

once you find "n", then to get "y" when x = 8, well \(\bf x=8\qquad y=\cfrac{{\color{red}{ n}}}{x}\implies y=\cfrac{{\color{red}{ n}}}{8}\)