SOLUTION: Good Morning, I have a mark-up problem that is haunting me. Could you please show me how to set it up correctly? I can't seem to figure it out. Here it is: A pair of shoes

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Question 752253: Good Morning,
I have a mark-up problem that is haunting me. Could you please show me how to set it up correctly? I can't seem to figure it out. Here it is:
A pair of shoes costs the retailer $85 per pair. At what price should the retailer mark them so he can sell them at a 15% disoount off the selling price and still make a 20% profit on his cost?
My brain is frozen on this.
Thank you in advance for your help.
Kindest regards,
Michelle Dean
Found 2 solutions by KMST, josmiceli:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= marked "original" price (in $)
discounted price = x-0.15x=0.85x
The profit would be the discounted price minus the cost,
profit =0.85x-85
As a percentage of the $85 cost, the profit would be
%280.85x-85%29%2F85x100%=20% or
%280.85x-85%29%2F85=0.20 --> 0.85x-85=0.20%2A85 --> 0.85x-85=17 --> 0.85x=85%2B17 --> 0.85x=102 --> x=102%2F0.85 --> highlight%28x=120%29
The retailer should mark the original price as $120.
The customer would get a 15% discount, which would reduce the price by $18, to $102.
Selling the shoes at $102, the retailer would have a profit of
$102 - $85 = $17, and that $17 is 20% of the $85 cost.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The wording is very tricky here. The way I read it is
that the retailer is going to mark the shoes at a
price, say +p+. Then he plans later to mark them
down by 15%. If he then sells them he wants to
make 20% above what he paid for them.
-----------------------------------
So, +p+-+.15p+=+.85p+ is what he actually sells them for.
He wants this sale to equal +85+%2B+.2%2A85+=+102+
I can say
+.85p+=+102+
+p+=+120+
He must mark them at $120
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Hope I got it- strange worded problem