Chapter 9.5, Problem 48HP

To determine

To identify the correct proportion and explain the reason.

Answer to Problem 48HP

J’s proportion matches with the correct proportion, S’s made mistake in obtaining expression for k she has written $k=\frac{z_1{x}_1}{y_1}\text{ and k}=\frac{z_2{x}_2}{y_2}$ which is incorrect because according to this equation z inversely varies as x and z directly varies as y which violates the given statement.

Explanation of Solution

Given information:

The given statement is that the combined variation in which z varies directly as x and z varies inversely as y

First obtain the correct proportion

  $\begin{array}{l}{z}_1=\frac{k{x}_1}{y_1}\text{ and }{z}_2=\frac{k{x}_2}{y_2}\\ k=\frac{z_1{y}_1}{x_1}\text{ and k}=\frac{z_2{y}_2}{x_2}\\ \frac{z_1{y}_1}{x_1}=\frac{z_2{y}_2}{x_2}\end{array}$

J’s proportion matches with the correct proportion, S’s made mistake in obtaining expression for k she has written $k=\frac{z_1{x}_1}{y_1}\text{ and k}=\frac{z_2{x}_2}{y_2}$ which is incorrect because according to this equation z inversely varies as x and z directly varies as y which violates the given statement.