money and sales

Question

An item is on sale at a discounted rate of 25% . With a sales tax of 8.75%, which fo the two ways of charging will be better for the customer: taking the discount first then charge the sales tax or charge the sales tax first then take the discount.
Please discuss thoroughly how you come up with your answer

Answer 1

Hello, Nicole

 

The answer to your question is that it does not make a difference.  You pay the same amount.  This is how.  Lets say that the item cost $100.  With the 25%, discount you will be paying $75 without the tax.  A 8.75% sales tax on an item that cost $75 dollars (the new price after the 25% discount) is $6.56 (6.5625 to be exact). So, you will end up paying 75+6.56=81.56. (you get 6.56 by multiplying 75*.0875).

 

Now, lets include the tax first and then the discount.  If the tax is 8.75% and the item cost $100, you will end up paying $108.75, with the tax.  Now, lets take a 25 discount.  That will be (0.25)(108.75)= 27.19 (or 27.1875).  The 27.19 represent the money discount.  So take the price, including the tax. 108.75-27.19= 81.56

 

So, we pay the same amount.

 

I hope this helps out. Take care, and don't forget to rate my answer.

 

D. Y. Taylor

Answer 2

Nicole, this is actually fairly easy, I promise!

 

Let's start with a simple price of $100.  Knowing that percent means "for each 100," we know that 25% of 100 is 25, so the new price is $75.

 

The word "of" in a problem always means to multiply.  75 x .0875 = $6.56, so our final price after tax is $81.56.

 

Now, let's do the tax first.  If we add the 8.75% tax to the $100, then we know our price is 108.75.  To make the math easier, if we take 25% off something, then we have 75% left, right?  Instead of multiplying by .25 and then subtracting, we are going to just multiply by .75.

 

108.75 x .75 = $81.56

 

Another way to look at it is that if we add 8.75% sales tax to something, the new total is 108.75% of the original, right?  If we then take 75% of that, we multiply 1.0875 x .75.  

 

If we take the 75% first, then the new price is 3/4 of the original price, or .75.  If we then add the 8.75% tax to the 75%, the new amount is 108.75% of the 75%, so we multiply .75 x 1.0875.

 

We all know that 1.0875 x .75 = .75 x 1.0875.  Make sense?