Chapter 9, Problem 40SGR

To determine

To find: $y$ when $x=-5$ .

Answer to Problem 40SGR

  $y=-10.5$

Explanation of Solution

Given information:

If $y$ varies inversely as $x$ and $y=15$ when $x=3.5$ .

Calculation:

Since, $y$ varies inversely as $x$ , therefore,

  $\begin{array}{l}xy=\text{constant or}\\ \frac{x_1}{y_2}=\frac{x_2}{y_1}\end{array}$

Here, $x_1=3.5$ , $y_1=15$ and $x_2=10$ . Therefore,

  $\begin{array}{l}\frac{3.5}{y_2}=\frac{-5}{15}\text{ (Direct variation)}\\ 3.5\left(15\right)=-5y_2\text{ (Cross multiply)}\\ 52.5=-5y_2\text{ (Simplify)}\\ -\frac{52.5}{5}=y_2\text{ (Divide each sides by }-5\text{)}\\ -10.5=y_2\end{array}$

Thus, when $x=10$ , the value of $y$ is $-10.5$ .

Hence,

  $y=-10.5$