Question

The sale price S (in dollars) of an item is given by the formula S=L-rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).I’ve already solved problem (a) although I’m not sure if it’s correct but I need help with problem (b)The list price of the shirt is $30 and the sale price is $18. What is the discount rate?

Answer 1

Since the equation of the sale price S is

`S=L-rL`

a)

To solve for r add rL to both sides

`\begin{gathered} S+rL=L-rL+rL \\ S+rL=L \end{gathered}`

Subtract S from both sides

`\begin{gathered} S-S+rL=L-S \\ rL=L-S \end{gathered}`

Divide both sides by L

`\begin{gathered} (rL)/(L)=(L-S)/(L) \\ \\ r=(L-S)/(L) \end{gathered}`

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

`\begin{gathered} r=(30-18)/(30) \\ \\ r=(12)/(30) \\ \\ r=(2)/(5) \\ \\ r=0.4 \end{gathered}`

The discount rate is 0.4