With the discount of 18% and tax included, the price of a sofa set is $4,826.52. Find the original price of the sofa set.

Question

Is the tax included on the 18%? if the tax rate is 8%, does that make the discount 10% or is it still 18% plus 8% tax?

Answer 1

The price of a retail item is displayed on a tag, on the shelf, on the menu, etc.

A discount to the price is often expressed as a percent [of the listed, base price].

Tax is applied to the sales total (either base price or discounted price) and is not kept by the retailer, but is passed on to the state, city, or other taxing authority.

These reasons explain why you often see prices just under a round dollar amount, like $19.95, so you will think the item costs you less than $20 when, with tax, you pay more than $20.

With word (story) problems, try to assign a variable to the value that the problem asks to be reported.  In this problem, it is “the original price of the sofa set.”  Let that be P.

The discount, 18% of P, is subtracted from P.  Then, tax (you mentioned 8%) is applied.  The total amount paid is $4,826,52.  In math terms, 
                 Sales Price   +     tax on sales price    =    total paid
                 (P – 18%P)  +     ( P – 18%*P )*8%     =  $4826.52          (note 8% is 0.08 or 8/100)
                      (P – 18%P) * 1.08  =   4826.52           (collect percent terms)
                                  0.82P*1.08 =  4826.52             (collect P terms)
                                             P = $5450.00             (divide both sides by 0.82*1.08)

Checking (very important)”
             A discount of 18% of $5450 is $981.    The discounted price is $4469.00
                    With 8% tax applied to $4469.00, the sales total is $4826.52              Check!

Q: Is tax included on the 18%?   A: No, the 18% discount is given by the retailer.

Q: Does that make the discount 10% or is it still 18% plus 8% tax?   A: Discounts are based on sales price (the “base”  of a percent calculation).  Actually, the customers pays somewhat less than they might have paid before the discount, but that is simply the customer’s perspective, not the sales price adjustment or the sales total.

Answer 2

Discount means that we pay less than the original price.  Tax means that we pay more than the original price.  We can write an algebraic equation to represent this.

 

Let x = the original price of sofa

 

 

Since the tax and discounted is include in the count, we have to take both of them into consideration.  Take the discount of the sofa, then add the tax to the result.

 

The price after the discount is  (x - 0.18x).  Add the tax rate to this new price.

 

x - 0.18x + 0.08(x - 0.18x) = 4826.52

 

 

Solve for x.  Combine like terms on the left side of the equation.

 

x - 0.18x + 0.08x - 0.0144x = 4826.52

 

0.8856x = 4826.52

 

 

Divide both sides of the equation by 0.8856

 

x = 5450

 

 

The original price of the sofa set is $5,450. 

 

As for your other question, if the tax rate is 8%, then the discount is still 18%.  As I mentioned earlier, the discount and tax rate is combined.  So whether you take the discount first, or the tax rate first, you should end up with the same result.