Chapter 8.5, Problem 8PPS

To determine

To find the value of $x_2$ .

Answer to Problem 8PPS

the value of $x_2$ is $-\frac{88}{3}$

Explanation of Solution

Given information:

x varies directly as y

the value of $x_1=11\text{ when }{y}_1=-3$

Calculation:

The values of $x_2$ can be obtained as

Use a proportion that relates the value

  $\begin{array}{l}\frac{x_1}{y_1}\text{=}\frac{x_2}{y_2}\left[\text{since,direct variation}\right]\\ \end{array}$

Put the values of $x_1=11$ , $y_1=-3$ , $y_2=8$ in above equation

  $\begin{array}{l}\frac{11}{-3}=\frac{x_2}{8}\\ \left(11\right)\left(8\right)=\left(-3\right)\left(x_2\right)\left[\text{cross multiply}\right]\\ 88=-3x_2\left[\text{simplify}\right]\\ x_2=-\frac{88}{3}\\ x_2=-\frac{88}{3}\end{array}$

Hence,

the value of $x_2$ is $-\frac{88}{3}$