A pair of sunglasses costs the retailer $80 per pair. At what price should the retailer mark them so he can sell them at a 20% discount off the selling price and still make a 20% profit on his cost?

Question

A pair of sunglasses costs the retailer $80 per pair.  At what price should the retailer mark them so he can sell them at a 20% discount off the selling price and still make a 20% profit on his cost?

anonymous · Answer

cost price of glasses = 80
he wants to make 20% profit  ie. 20% of 80 = 0.20*80 = 16
selling price = 80+16 = 96

let the marked price = x
discount = 20% of x = 0.20x
selling price = marked price - discount = x - 0.20x = 0.80x

ATQ 0.80x = 96
x = 96/0.80
x = 120

so the marked price will be $120