Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.8 - Modeling Using Variation - Exercise Set - Page 423: 19


The required equation is $x=k\frac{z}{\left( y-w \right)}$ and the value of $y$ is $\frac{kz+xw}{x}$.

Work Step by Step

As the value of $x$ varies directly as $z$ and inversely as $\left( y-w \right)$ , we have $x=k\frac{z}{\left( y-w \right)}$ Where $k$ is a constant. Now, solve the above equation for $y$. $\begin{align} & x=k\frac{z}{\left( y-w \right)} \\ & x\left( y-w \right)=kz \\ & xy-xw=kz \\ & xy=kz+xw \end{align}$ Solving further, we get $y=\frac{kz+xw}{x}$
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