Question

the volume V of a gas held at a constant temperature in a closed container varies inversely with its pressure P. if the volume of a gas is 600 cubic centimeters when the pressure is 200, find the volume when the pressure is 150

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{{\color{red}{ \textit{some value }}}}{\textit{something else}}\\ \quad \\
y&=\cfrac{{\color{red}{ n}}}{x}
&&\implies y=\cfrac{{\color{red}{ n}}}{x}
\end{array}
\\ \quad \\
v=\cfrac{{\color{red}{ n}}}{p}\qquad v=600\qquad p=200\implies 600=\cfrac{{\color{red}{ n}}}{200}
\)

solve for "n" to find the "constant of inverse variation"
once you find that, plug it in your inverse variation equation

to find "v" when "p = 150" well, set p = 150 :) , that is \(\bf v=\cfrac{{\color{red}{ n}}}{150}\)