Chapter 9, Problem 26PT

To determine

To find: $n$ when $m=30$ .

Answer to Problem 26PT

When $m=30$ , the value of $n$ is $-\frac{15}{4}$ .

Explanation of Solution

Given information:

If $m$ varies directly as $n$ and $m=24$ when $n=-3$ .

Calculation:

Since, $m$ varies directly as $n$ , therefore,

  $\begin{array}{l}\frac{m}{n}=\text{constant or}\\ \frac{m_1}{n_1}=\frac{m_2}{n_2}\end{array}$

Here, $m_1=24$ , $n_1=-3$ and $m_2=10$ . Therefore,

  $\begin{array}{l}\frac{24}{-3}=\frac{30}{n_2}\text{ (Direct variation)}\\ 24\left(n_2\right)=30\left(-3\right)\text{ (Cross multiply)}\\ 24n_2=-90\text{ (Simplify)}\\ n_2=\frac{-90}{24}\text{ (Divide each sides by 24)}\\ n_2=-\frac{15}{4}\end{array}$

Thus, when $m=30$ , the value of $n$ is $-\frac{15}{4}$

Hence,

When $m=30$ , the value of $n$ is $-\frac{15}{4}$ .