A company marks up the cost of all items by 28%. If they want to have a sale, what is the maximum they can reduce the selling price by before going below cost?

Question

It's a margin/markup question.

Selling Price = Cost - Markup

 (the maximum percentage - just ran out of space in the question box)

Answer 1

Hi Teagan,

 

This problem reminds you that if you increase a number by a certain percentage, you have to decrease it be a different percentage to get the same number.

 

An easy example is increasing a number by 100% which doubles it.  So if you increase 10 by 100%, you get 20.  To get back to 10, you have to decrease 20 by half of its value, or 50%.

 

So the easiest way to solve the problem, is to substitute  real number.  Let's choose an easy one . . . 100.

 

Marking up the cost by 28% means you have 28% of 100 to it.  28% of 100 is 28 and 100 + 28 = 128.

 

Now to get back to 100, you have to figure what percent of 128 is 28 and subtract it.

 

Let's set up a proportion:  28 is to 128 as X is to 100--> 28/128 = X/100

 

Cross multiply--> 2800 = 128X

 

Divide both sides by 128--> X = 21.875 percent