23. The marked price of a jacket is 60% higher than the cost. If the jacket is sold at a discount of 30% and the
profit of selling the jacket is $30, find the marked price of the jacket.
Let's call the cost of the jacket C.
The marked price of the jacket is C + 60% of C = C + 0.6C = 1.6C.
The jacket is sold at a discount of 30%, so the selling price is 70% of the marked price: 0.7 * 1.6C = 1.12C.
The profit from selling the jacket is the selling price minus the cost: 1.12C - C = 0.12C.
We are told that the profit is $30, so 0.12C = $30.
Dividing both sides of the equation by 0.12, we have C = $250.
The marked price of the jacket is 1.6C = 1.6 * $250 = $<<1.6*250=400>>400. Answer: \boxed{400}.
Let's find the cost price first:
Let the cost price of the jacket be x.
According to the given information, the marked price of the jacket is 60% higher than the cost.
So, the marked price of the jacket is x + 0.6x = 1.6x.
Now, the jacket is sold at a discount of 30%.
So, the selling price of the jacket is 1.6x - (0.3 * 1.6x) = 1.6x - 0.48x = 1.12x.
We are also given that the profit of selling the jacket is $30.
Profit = Selling Price - Cost Price.
$30 = 1.12x - x,
$30 = 0.12x.
Now, let's solve for the value of x.
x = $30 / 0.12,
x = $250.
Therefore, the cost price of the jacket is $250.
To find the marked price of the jacket, we can substitute the value of x in the equation of the marked price:
Marked price = 1.6x = 1.6 * $250 = $400.
Therefore, the marked price of the jacket is $400.
To find the marked price of the jacket, we need to follow a step-by-step process:
Step 1: Determine the cost of the jacket.
Let's assume the cost of the jacket is 'C'.
Step 2: Calculate the marked price of the jacket.
Since the marked price is 60% higher than the cost, we can calculate it using the formula:
Marked Price = Cost + (60% of Cost) = C + 0.6C = 1.6C
Step 3: Calculate the selling price of the jacket after a 30% discount.
The selling price is the marked price minus the discount. In this case, the discount is 30%, so the selling price can be calculated as:
Selling Price = Marked Price - (30% of Marked Price)
= 1.6C - (0.3 * 1.6C)
= 1.6C - 0.48C
= 1.12C
Step 4: Determine the profit from selling the jacket.
Given that the profit from selling the jacket is $30, we can equate it to the difference between the selling price and the cost:
Profit = Selling Price - Cost
$30 = 1.12C - C
$30 = 0.12C
Step 5: Solve for the cost of the jacket.
To find the cost, divide both sides of the equation by 0.12:
C = $30 / 0.12
C = $250
Step 6: Calculate the marked price of the jacket.
Once we have the cost, we can substitute it into the formula we derived in Step 2 to find the marked price:
Marked Price = 1.6C
= 1.6 * $250
= $400
Therefore, the marked price of the jacket is $400.