Question

A particular style of sunglasses costs the retailer $85 per pair. At what price should the retailer mark them so he can sell them at a 15% discount off the original price and still make 20% profit on his cost?

Answer 1

Given that a particular style of sunglasses costs the retailer $85 per pair.

This implies that

`cost\text{ price = \$85}`

To make a profit of 20% on his cost, he has to sell at the price of

`\begin{gathered} \$85\text{ +\lparen}(20)/(100)*85) \\ =\$102 \end{gathered}`

To determine the mark price for which he can sell them at a 15% discount off the original price,

let

`y\Rightarrow mark\text{ price}`

Thus,

`\begin{gathered} y-((15)/(100)* y)=102 \\ \Rightarrow y-0.15y=102 \\ 0.85y=102 \\ divide\text{ both sides by the coefficient of y, which is 0.85} \\ (0.85y)/(0.85)=(102)/(0.85) \\ \implies y=\$120 \end{gathered}`

Therefore. the retailer should mark the price at $120.