Chapter 9.5, Problem 3CYP

To determine

To find the value of $x_2$ .

Answer to Problem 3CYP

the value of $x_2$ is $8$

Explanation of Solution

Given information:

x varies inversely as y

the value of $x_1=24$ when $y_1=4$

Calculation:

The value of $x_2$ can be obtained as

Use a proportion that relates the values

  $\frac{x_1}{y_2}=\frac{x_2}{y_1}$ [ since, inverse variation]

Put the values of $x_1=24$ , $y_1=4$ ,and $y_2=12$ in above equation

  $\begin{array}{l}\frac{24}{12}=\frac{x_2}{4}\\ \left(24\right)\left(4\right)=x_2\left(12\right)\left[\text{cross multiply}\right]\\ 96=12x_2\left[\text{simplify}\right]\\ x_2=8\left[\text{divide each side by 12}\right]\end{array}$

Hence,

the value of $x_2$ is $8$