Final answer:
To determine the final purchase cost, apply successive discounts of 9% and 6% to the original cost to get $30,794.40. For the selling price, add a 21% profit and 25% overhead expenses to the purchase cost to arrive at $44,959.82.
Step-by-step explanation:
The problem to solve is to determine the cost after discounts and the selling price including profit and overhead expenses for a clothing merchant. Initially, the merchant purchases a shipment of clothes for $36,000.
The first step is to apply the discounts of 9% and 6%. The discounts are applied successively, meaning the second discount is applied to the already reduced amount after the first discount.
Calculating the Purchase Cost
The first discount of 9% on the original cost of $36,000:
First discount = 9% of $36,000 = 0.09 * $36,000 = $3,240.
Reduced price after first discount = $36,000 - $3,240 = $32,760.
Next, apply the second discount of 6% to the reduced price:
Second discount = 6% of $32,760 = 0.06 * $32,760 = $1965.60.
Final purchase cost = $32,760 - $1965.60 = $30,794.40.
Calculating the Selling Price
Now, we must calculate the selling price that includes a 21% profit on the purchase cost and 25% overhead expenses on the purchase cost:
Profit = 21% of $30,794.40 = 0.21 * $30,794.40 = $6,466.82.
Overhead = 25% of $30,794.40 = 0.25 * $30,794.40 = $7,698.60.
The selling price = Purchase cost + Profit + Overhead = $30,794.40 + $6,466.82 + $7,698.60 = $44,959.82