Question

A particular style of sunglasses costs the retailer $70 $⁢70 per pair. At what price should the retailer mark them so he can sell them at a 10% 10% discount off the original price and still make 35% 35% profit on his cost?

Answer 1

After the 10% discount on marked price (P), the selling price is ...

... P×(100% -10%) = 0.90P

After a markup off 35% on cost, the value is

... $70×(100% +35%) = 1.35×$70 = $94.50

The retailer wants these two values to be equal:

... 0.90P = $94.50

... P = $94.50/0.90 = $105.00 . . . . . divide by the coefficient of P

The marked price should be $105.00.