at a boutique, an evening gown is marked at a profit of 40% on the cost price. it is sold in a sale at 20% discount.
a. Find the actual profit as a percentage of the cost price.
b. if a customer bought it for $448, find
i. the marked price
ii. the actual profit
let the cost price be x
original selling price = x + .4x or 1.4x
after 20% discound ...
final selling price = (.8)(1.4x) = 1.12x
which looks like a 12% profit based on cost
b) if x = 448
If by "marked" price you mean final selling price, then
1.12(448) = 501.76
actual profit = 501.76-448 = 53.76
or
.12(448) = 53.76
To find the answers, we can break down the calculations step by step:
a. To find the actual profit as a percentage of the cost price, we need to find the difference between the selling price and the cost price, and then calculate the profit percentage.
Let's assume the cost price of the evening gown is $x.
The evening gown has a markup of 40% on the cost price. So, the marked price is:
Marked Price = Cost Price + 40% of Cost Price
= x + (40/100) * x
= 1.4x
Now, the evening gown is sold at a discount of 20%. The selling price after the discount can be calculated as:
Selling Price = Marked Price - 20% of Marked Price
= 1.4x - (20/100) * 1.4x
= 1.4x - 0.28x
= 1.12x
The actual profit is the difference between the selling price and the cost price:
Actual Profit = Selling Price - Cost Price
= 1.12x - x
= 0.12x
To find the actual profit as a percentage of the cost price, we divide the actual profit by the cost price and multiply by 100:
Actual Profit Percentage = (Actual Profit / Cost Price) * 100
= (0.12x / x) * 100
= 12%
Therefore, the actual profit as a percentage of the cost price is 12%.
b. i. If a customer bought the gown for $448, we can find the marked price by reversing the calculations above.
We know that Selling Price = Marked Price - Discounted Amount
$448 = Marked Price - 20% of Marked Price
Let's solve this equation to find the marked price:
$448 = Marked Price - 0.2 * Marked Price
$448 = Marked Price * (1 - 0.2)
$448 = Marked Price * 0.8
Marked Price = $448 / 0.8
Marked Price = $560
Therefore, the marked price of the evening gown was $560.
b. ii. To find the actual profit when the gown was bought for $448, we can use the calculations from part 'a'.
Actual Profit = Selling Price - Cost Price
= $448 - Cost Price
Since we know the actual profit percentage is 12%, we can set up the equation:
12% of Cost Price = $448 - Cost Price
Let's solve this equation to find the actual profit:
0.12 * Cost Price = $448 - Cost Price
0.12 * Cost Price + Cost Price = $448
1.12 * Cost Price = $448
Cost Price = $448 / 1.12
Cost Price = $400
Therefore, the actual profit when the gown was bought for $448 is $400 - $400 = $0.
I hope this explanation helps you understand how to calculate the actual profit percentage and solve the given problem. Let me know if you have any further questions!