Markups and Markdowns

Question

Bari Jay, a gown manufacturer, received an order for 400 prom dresses from China. Her cost is $29 a gown. If her markup based on selling price is 73%, what is the selling price of each gown? (Round your answer to the nearest cent.)

Answer 1

400 dresses? What a great order, Bari must be happy today! :-)

I'm not sure about your question because usually "markup" (it's a mark UP because you're adding to the cost price) is based on your purchase price, or "unit cost". So the wording used here is, unfortunately, a little ambiguous.

The standard formula is markup % = ( (selling price - unit cost) / unit cost ) x 100

This means in Bari's case 73% = (S - 29) / 29 x 100

=> 0.73 x 29 = (S - 29)

=> 0.73 x 29 + 29 = S

=> S = $50.17

A markup of 73% in this way means adding 73% of the purchase price to the purchase price to get your selling price (i.e. $29 + $21.17 = $50.17). In this case, her profit per dress is $21.17, and you could easily figure out her total profit for 400 dresses.

However, as the question refers to the markup "based on selling price", I think we're looking to do the calculation a slightly different way. This can be called markup based on selling price (or "markdown"), but usually would be referred to as a "profit" or "product margin" or similar.

Whatever you prefer to call it, here's the formula:

Product Margin % = ( (Selling Price - Unit Cost) / Selling Price ) x 100

In this case:

73% = ( (S - 29) / S ) x 100

=> S = $107.41

And with this price, Bari makes $78.41 per dress (i.e. $29 + $78.41 = $107.41).

Leaving terminology aside, the key issue is that you can look at pricing in relation to either the cost price or the sales price. Using a very simple example might be helpful.

If you buy a widget for $50 and sell it for $100, your profit is the difference, $50.

But you can say that you had a markup of 100% (100-50 / 50 ) or a profit margin (or markup based on selling price) of 50% (100-50 / 100).