a dealer makes a profit of 25% when he sells a shirt at a discount of 30%. if the profit is 91, find the marked price of this shirt.
if the cost is c and the marked price is p, then
.70 * p = 1.25c = c+91
.25c = 91
c = 364
p = 1.25*364/.7 = 650
To find the marked price of the shirt, we can follow these steps:
Step 1: Calculate the selling price of the shirt.
Since the dealer makes a profit of 25%, the selling price of the shirt will be 100% (original cost price) + 25% (profit percentage). Therefore the selling price is 125% of the cost price.
Step 2: Calculate the cost price of the shirt.
The selling price is at a discount of 30%, so it is equal to 70% of the marked price.
We can set up the equation: selling price = 70% of the marked price.
Step 3: Find the cost price.
Since the selling price is 125% of the cost price, we can set up the equation:
125% of the cost price = 70% of the marked price.
Step 4: Solve for the cost price.
Divide both sides of the equation by 125 to isolate the cost price:
Cost price = (70% of the marked price) / 125%.
Step 5: Calculate the marked price.
Divide the profit by the profit percentage (25%) to obtain the cost price:
Marked price = Cost price + Profit.
Let's calculate the marked price using the given profit of 91 and the provided information of a 30% discount and 25% profit.