Sales and Taxes

Date: 03/11/2001 at 19:39:30
From: Aiziah
Subject: Sales and Taxes

I bought $27.97 worth of food. The food tax is 5.5%. I'm trying to 
find the tax I have to pay, and the total amount that I pay.

Date: 03/13/2001 at 01:09:50
From: Doctor Ian
Subject: Re: Sales and Taxes

Hi Aiziah,

There are a couple of ways that you might go about that. The usual way 
would be to multiply the amount of the purchase ($27.97) by the tax 
(5.5%, or 0.055), and add the two together:

  total = $27.97 + 0.055 * $27.97

        = $27.97 * (1 + 0.055)

        = $27.97 * 1.055

Another way to look at it is this: If the amount of the purchase were 
exactly $100, then you would have to pay exactly $5.50 in tax. So the 
amount of tax that you're actually going to pay is the same fraction 
of $5.50 that $27.97 is of $100:

   tax    $27.97
  ----- = ------ 
  $5.50    $100

          27.97 * 5.50
    tax = -------------
              100

                  5.50
        = 27.97 * ----
                  100

        = 27.97 * 0.055

which is the same thing we got with the first method. (That should 
come as no surprise, right?)  Actually, this tells you _why_ the first 
method works, which is a handy thing to know in case you forget some 
of the tricks for working with percentages. 

I hope this helps.  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/