Chapter 8.2, Problem 13OE

To determine

To explain: Variations in z according to the given situation.

Answer to Problem 13OE

If x is halved and y is quadrupled, z is doubled.

Explanation of Solution

Given information:

The following variation:

z varies jointly as x and y.

The following situation:

x is halved and y is quadrupled.

Calculation:

The given variation can be expressed as an equation as follows:

  $z=kxy$

where k is a constant.

If x is halved and y is quadrupled, the equation can be written as:

  $\begin{array}{l}z=kxy[\text{Equation]}\\ z=k\left(\frac{x}{2}\right)\left(4y\right)[\text{Half }x\text{ and quadruple }y]\\ z=2kxy[\text{Simplify]}\end{array}$