A particular style 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 30% profit on his cost?
To determine the selling price, we need to consider two factors: the desired profit and the discount.
Step 1: Calculate the desired profit:
Profit = Cost * Profit Margin
Profit = $80 * 0.30 = $24
Step 2: Determine the selling price without considering the discount:
Selling Price = Cost + Profit
Selling Price = $80 + $24 = $104
Step 3: Calculate the selling price after applying the discount:
Discount = Selling Price * Discount Percentage
Discount = $104 * 0.20 = $20.80
Final Step: Determine the marked price by adding the discount to the selling price:
Marked Price = Selling Price + Discount
Marked Price = $104 + $20.80 = $124.80
Therefore, the retailer should mark the sunglasses at $124.80 so that he can sell them at a 20% discount off the selling price and still make a 30% profit on his cost.
To determine the appropriate selling price, let's break down the problem step by step.
Step 1: Calculate the desired profit.
The retailer wants to make a 30% profit on the cost of the sunglasses. The profit can be calculated by multiplying the cost by the profit percentage:
Profit = Cost * Profit Percentage
Profit = $80 * 0.30
Profit = $24
Step 2: Determine the total cost.
To calculate the total cost, we need to add the profit to the cost:
Total Cost = Cost + Profit
Total Cost = $80 + $24
Total Cost = $104
Step 3: Calculate the selling price before the discount.
Since the retailer wants to offer a 20% discount off the selling price, the original selling price needs to be calculated. Let's call it "x."
Selling Price = Cost + Profit
x = $80 + $24
x = $104
Step 4: Adjust for the discount.
To determine the final selling price after applying a 20% discount, we need to subtract 20% from the original selling price. Let's call it "y."
Discounted Selling Price = x - (x * Discount Percentage)
y = $104 - ($104 * 0.20)
y = $104 - $20.80
y = $83.20
Therefore, the retailer should mark the sunglasses at $83.20, allowing a 20% discount off the selling price while still making a 30% profit on the cost.
.80x = 80*1.30
x = 130