Since the equation of the sale price S is
[tex]S=L-rL[/tex]
a)
To solve for r add rL to both sides
[tex]\begin{gathered} S+rL=L-rL+rL \\ S+rL=L \end{gathered}[/tex]
Subtract S from both sides
[tex]\begin{gathered} S-S+rL=L-S \\ rL=L-S \end{gathered}[/tex]
Divide both sides by L
[tex]\begin{gathered} \frac{rL}{L}=\frac{L-S}{L} \\ \\ r=\frac{L-S}{L} \end{gathered}[/tex]
b)
Since the list price of the shirt is $30, then
L = 30
Since the sale price is $18, then
S = 18
Substitute them in the equation of r to find it
[tex]\begin{gathered} r=\frac{30-18}{30} \\ \\ r=\frac{12}{30} \\ \\ r=\frac{2}{5} \\ \\ r=0.4 \end{gathered}[/tex]
The discount rate is 0.4
