Chapter 12.8, Problem 1WE

To determine

To calculate: the value of, $c$ , where $a=36\text{and}b=25$ .

  $c$ varies directly as $a$ and inversely as $b$ . If $c=15$ when $a=18$ and $b=40$ .

Answer to Problem 1WE

The value of $c$ is $48$ .

Explanation of Solution

Given information:

The value of, $c$ , where $a=36\text{and}b=25$ .

  $c$ varies directly as $a$ and inversely as $b$ . If $c=15$ when $a=18$ and $b=40$ .

Calculation:

Consider the values,

The value of, $c$ , where $a=36\text{and}b=25$ .

  $c$ varies directly as $a$ and inversely as $b$ . If $c=15$ when $a=18$ and $b=40$ .

Recall that the $c$ ,varies directly as $a$ and inversely as $b$ , then $a$ will be in the numerator while $b$ is in the numerator while $b$ is in the denominator of the equation then:

  $c=k\left(\frac{a}{b}\right)$

Here , If $c=15$ when $a=18$ and $b=40$ .

  $\begin{array}{c}c=k\left(\frac{a}{b}\right)\\ 15=k\frac{18}{40}\\ 15\left(40\right)=18k\\ 600=18k\end{array}$

From here the value of $k$ is:

  $\begin{array}{c}600=18k\\ \frac{600}{18}=k\\ \frac{100}{3}=k\end{array}$

Thus the equation of the variation is :

  $\begin{array}{l}c=\frac{\frac{100a}{3}}{b}\\ c=\frac{100a}{3b}\end{array}$

Now to find the value of $c$ when $a=36$ and $b=25$ .

Now apply these values in the above expression:

  $\begin{array}{c}c=\frac{100a}{3b}\\ c=\frac{100\cdot 36}{3\cdot 25}\\ c=\frac{3600}{75}\\ c=48\end{array}$

Thus, the value of $c$ is $48$ .