A pair of shoes with a manufacturer's price of $80 is marked up 115% and then sold to a customer at 65% off the mark up price. If a 10% tax is added to this cost, then the total price the customer paid for the shoes, in dollars, was....
I know the answer but don't understand it at all
80 * (1 + 1.15) * (1 - .65) * (1 + .10) = ?
price * mark up * discount * tax = total price paid
80 * 2.15 * 0.65 * 1.10 = 122.98
note that a 15% markup multiplies the price by 1.15 (the original amount + 15% of that amount: 1 + 0.15)
so, a 115% markup multiplies it by 2.15 (1 + 1.15)
oops. I didn't see the 65% off. That means they paid only 35%. So the real calculation is
80 * 2.15 * 0.35 * 1.10 = 66.22
To solve this problem, let's break it down step by step.
Step 1: Calculate the markup price
The manufacturer's price of the shoes is $80. To find the marked-up price, we need to calculate 115% of $80.
Markup Price = Manufacturer's Price + (Manufacturer's Price * Markup Percentage)
Markup Price = $80 + ($80 * 115%)
Markup Price = $80 + ($80 * 1.15)
Markup Price = $80 + $92
Markup Price = $172
Step 2: Calculate the discounted price for the customer
The shoes are sold to the customer at a 65% discount off the marked-up price. To find the discounted price, we need to calculate 65% of $172.
Discounted Price = Markup Price - (Markup Price * Discount Percentage)
Discounted Price = $172 - ($172 * 65%)
Discounted Price = $172 - ($172 * 0.65)
Discounted Price = $172 - $111.80
Discounted Price = $60.20
Step 3: Add the tax
A 10% tax is added to the discounted price. To find the total price after taxes, we need to calculate 10% of $60.20 and add it to $60.20.
Total Price = Discounted Price + (Discounted Price * Tax Percentage)
Total Price = $60.20 + ($60.20 * 10%)
Total Price = $60.20 + ($60.20 * 0.10)
Total Price = $60.20 + $6.02
Total Price = $66.22
Therefore, the total price the customer paid for the shoes is $66.22.