A particular style of sunglasses costs the retailer $85.00 per pair. At which price should the retailer mark them so he can sell them at a 15% discount off the original price and still make 25% profit on his cost
Don't know original price, but to make 25% profit, $85 * 1.25 = ?
original selling price ---- x
.85x = 1.25(85)
x = 125
The marked selling price should be $125
check:
selling price after discount = .85(125) = 106.25
profit = 106.25 - 85 = 21.25
percentage profit = 21.25/85 = .25 or 25%
looks good
0.85x = 85 * 1.25
so x = 85*1.25/0.85 = ____
To determine at which price the retailer should mark the sunglasses, we need to calculate both the selling price and the desired profit margin.
Step 1: Calculate the desired profit margin:
The retailer wants to make a 25% profit on his cost. The cost of the sunglasses for the retailer is $85.00 per pair. Therefore, the desired profit margin can be calculated by multiplying the cost by the profit percentage:
Profit Margin = Cost * Profit Percentage
Profit Margin = $85.00 * 0.25
Profit Margin = $21.25
Step 2: Calculate the selling price:
Since the retailer wants to offer a 15% discount off the original price, the selling price can be calculated by subtracting the discount amount from the original price:
Discount Amount = Original Price * Discount Percentage
Discount Amount = Original Price * 0.15
Discounted Selling Price = Original Price - Discount Amount
The discounted selling price should also include the desired profit margin. Therefore, the selling price can be calculated by adding the profit margin to the discounted selling price:
Selling Price = Discounted Selling Price + Profit Margin
Step 3: Calculate the original price:
To find the original price, we need to reverse the calculation by dividing the selling price by (1 - discount percentage):
Original Price = Selling Price / (1 - Discount Percentage)
Let's calculate the selling price and original price:
Discount Amount = $85.00 * 0.15
Discount Amount = $12.75
Discounted Selling Price = $85.00 - $12.75
Discounted Selling Price = $72.25
Selling Price = $72.25 + $21.25
Selling Price = $93.50
Original Price = $93.50 / (1 - 0.15)
Original Price = $109.41
Therefore, the retailer should mark the sunglasses at a price of $109.41 in order to sell them at a 15% discount off the original price and still make a 25% profit on the cost.