Chapter 9, Problem 27PT

To determine

To find: $s$ when $r=7$ and $t=2.5$

Answer to Problem 27PT

The value of $s$ is $-2$ .

Explanation of Solution

Given information:

If $r$ varies jointly as $s$ and $t$ , and $s=20$ and $r=140$ when $t=-5$

Calculation:

Since, $r$ varies jointly as $s$ and $t$ , therefore,

  $\begin{array}{l}\frac{st}{r}=\text{constant or}\\ \frac{s_1{t}_1}{r_1}=\frac{s_2{t}_2}{r_2}\end{array}$

Here, $s_1=20$ , $r_1=140$ , $t_1=-5$ , $r_2=7$ , $t_2=2.5$ . Therefore,

  $\begin{array}{l}\frac{20\cdot \left(-5\right)}{140}=\frac{s_2\left(2.5\right)}{7}\text{ (Joint variation)}\\ \frac{-5}{7}=\frac{2.5s_2}{7}\text{ (Simplify)}\\ -5\left(7\right)=2.5s_2\left(7\right)\text{ (Cross multiply)}\\ -35=17.5s_2\text{ (Simplify)}\\ \frac{-35}{17.5}=s_2\text{ (Divide both sides by 17}\text{.5)}\\ -2=s_2\end{array}$

Thus, the value of $s$ is $-2$ .

Hence,

The value of $s$ is $-2$ .