Chapter 1.5, Problem 31E

To determine

To calculate:

The solution for number of completed passes $C$

Answer to Problem 31E

The solution for number of completed passes $C$ is $C=A\left(\frac{R}{5}+0.3\right)$ .

Explanation of Solution

Given information:

  $R=5\left(\frac{C}{A}-0.3\right)$

Calculation:

The given formula for completion rating is:

  $R=5\left(\frac{C}{A}-0.3\right)$......................... (1)

Now need to write the equation in the form of $C$ , so:

Switch sides of eq. (1):

  $5\left(\frac{C}{A}-0.3\right)=R$

Now divide by $5$ :

  $\begin{array}{l}\frac{5}{5}\left(\frac{C}{A}-0.3\right)=\frac{R}{5}\\ \frac{C}{A}-0.3=\frac{R}{5}\end{array}$

Now add $0.3$ on both sides of above equation:

  $\begin{array}{l}\frac{C}{A}-0.3=\frac{R}{5}\\ \frac{C}{A}-0.3+0.3=\frac{R}{5}+0.3\\ \frac{C}{A}=\frac{R}{5}+0.3\end{array}$

Multiply by $A$ :

  $\begin{array}{l}\frac{C}{A}\times A=A\left(\frac{R}{5}+0.3\right)\\ C=A\left(\frac{R}{5}+0.3\right)\end{array}$