Answer
a. $\frac{L-S}{L}=r$
b. Discount rate is $0.40=40\%$.
Work Step by Step
The given formula is
$\Rightarrow S=L-rL$
a.
$\Rightarrow S=L-rL$
Subtract $L$ from each side.
$\Rightarrow S-L=L-rL-L$
Simplify.
$\Rightarrow S-L=-rL$
Divide each side by $-L$.
$\Rightarrow \frac{S-L}{-L}=\frac{-rL}{-L}$
Simplify.
$\Rightarrow \frac{L-S}{L}=r$ ...... (1)
b.
Sale price $S=\$18$.
List price $L=\$30$.
Substitute both values into the equation (1).
$\Rightarrow \frac{30-18}{30}=r$
Simplify.
$\Rightarrow \frac{12}{30}=r$
$\Rightarrow 0.40=r$
$\Rightarrow 40\%=r$
