Need explanations for these, how to solve later problems?

Question

anonymous · Answer

The discount on a new stereo was 200$. This was a discount of 23%. What was the original selling price of the stereo? 

The discount on a new stereo was 200$. This was a discount of 23%.What was the sale price? 

The discount on a new stereo was 200$. This was a discount of 23%. What would a customer pay for the stereo if a 7% sales tax was added to the sale price? 

I've had these kind of questions come up on all my test, but I have NO idea how to solve them! people have helped me get the answer but I need to know how to solve them for the future questions I will have.

b87lar · Answer

Any percentage always corresponds to a ratio. What ratio it is depends on the nature of the percentage, for example, in this case you can view a discount in two ways (one of which is a percentage): 
(1) discount is something subtracted from the retail price (original selling price): Retail - Discount = Sale 
(2) discount can be also expressed as percentage if you view it as percentage (or ratio, or relative quantity, which ever term you prefer): Discount / Retail = Percentage

b87lar · Answer

these two types (subtraction and ratio) is all you need to solve many of these problems. In this case we know the discount in both forms: Discount = Retail - Sale and Discount% = (Discount/Retail) *100%. The question is how much was retail. so:
Retail = Discount/(Discount%/100 ) = 200/0.23 = 869.57$

anonymous · Answer

Thanks!

b87lar · Answer

now that you know the retail price, you can use the difference point of view on discount: Retail-Discount = Sale. 869.57-200=669.57

b87lar · Answer

the last question (7% tax) is again the same exercise: percentage corresponds to a ratio of things: we know it's 7% of the sale price and we are looking for the amount that 7% means. so the Tax%=(SomeAmount/Sale)*100 => SomeAmount=Sale*Tax%/100. I get 46.87$ for the tax amount so the customer would pay 669.57+46.87

b87lar · Answer

(the 100 factor is there because of the definition of percentage. Normally, the "ratio of things" should be in [0,1])

anonymous · Answer

Thank you very much, once again! You've been a great help.