A particular style of jacket costs the retailer $90 per jacket. At what price should the retailer mark them so he can sell them at a 10% discount off the selli

Question

A particular style of jacket costs the retailer $90 per jacket. At what price should the retailer mark them so he can sell them at a 10% discount off the selling price and still make 20% profit on his cost?

Answer 1

"sell them at a 10% discount off the selling price and still make 20% profit on his cost"

 

That statement has two parts.

 

   Let x = selling price

 

"still make 20% profit on his cost" relates to the cost of $90.  It is:

       cost    +    20% of cost 

          1.20*cost                      [we can use 1.20 or 120/100 as needed in the problem]

          1.20*$90

             $108             [this is x, the selling price at which the retailer earns 20%]

 

Now, what is the marking price so the retailer can sell the jacket at 10% off the marked price [note word change]?

 

   Let y = the price to be marked

         marked price    -   10% of marked price    =     $108

                 y            - 0.1y                               = $108

                       0.9y                                        = $108

                    y = $108/0.9           [divide both sides by 0.9]

                    y = $120

 

If the retailer marks a price of $120 on the jacket and sells it for 10% off (that is, $120-$12=$108), there will still be a 20% profit because the cost was only $90 (and $90 + 20% of $90 is $108).