Chapter 1.5, Problem 33E

a.

To determine

To calculate:

The formula for $r$

Answer to Problem 33E

The formula for $r$ is $r=1-\frac{S}{L}$

Explanation of Solution

Given information:

  $S=L-rL$

Calculation:

The given formula for sale price in dollars is:

  $S=L-rL$......................... (1)

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

Switch sides of eq. (1):

  $\begin{array}{l}L-rL=S\\ L\left(1-r\right)=S\end{array}$

Now divide by $L$ :

  $\begin{array}{l}\frac{L}{L}\left(1-r\right)=\frac{S}{L}\\ 1-r=\frac{S}{L}\end{array}$

Subtract $1$ from both sides of equation:

  $\begin{array}{l}1-1-r=\frac{S}{L}-1\\ -r=\frac{S}{L}-1\end{array}$

Multiply by $-1$ :

  $\begin{array}{l}-\left(-1\right)r=\left(-1\right)\left(\frac{S}{L}-1\right)\\ r=1-\frac{S}{L}\end{array}$

b.

To determine

To calculate:

The discount rate for the shirt

Answer to Problem 33E

The discount rate for the shirt is $40\%$ .

Explanation of Solution

Given information:

  $\begin{array}{l}S=\$18\\ L=\$30\end{array}$

Calculation:

The given formula for sale price in dollars is:

  $S=L-rL$......................... (1)

Put the values to calculate the discount rate for the shirt:

  $\begin{array}{l}S=L-rL\\ 18=30-30r\\ 30r=30-18\\ 30r=12\\ r=\frac{12}{30}\\ r=0.4\\ r=40\%\end{array}$