Adding Tax and Tip

Date: 07/19/98 at 01:17:51
From: Steve K 
Subject: Formulas 

Hello Dr. Math,

I am a Senior Conference Services Manager at The Ritz-Carlton 
Phoenix. I am having a little trouble with a math formula and I could 
use your help. 

Most all of our food and beverage banquet prices are subject to a
taxable 20% hotel service charge as well as a local 6.8% sales tax.
We call these charges "Plus, Plus." For example, we can serve a group 
a deli buffet lunch at $25.00++ per person. I used to have a formula 
(a 1.???? number) that would add up and come up with the total amount. 

For example, the total of a $25.00 lunch is:

   $25.00 + $5 service charge + $2.04 tax = $32.04

In addition, I would like to know the backing out number (0.7????).

Please help.

Thank you.

Date: 07/19/98 at 04:34:40
From: Doctor Mike
Subject: Re: Formulas 
   
Hi, I think I can help. First, to get the total charge including the 
service charge you multiply by 1.20 (cost + 20% extra). Then multiply 
by 1.068 (total + 6.8% extra). To do that in one step you use the 
product of those numbers, (1.20)*(1.068) = 1.2816.  

To use your example, multiply 25 by 1.2816 to get 32.04 and divide 
32.04 by 1.2816 to back out the billed amount and get to the base cost. 
Dividing may be better than using a separate number, because that turns 
out to be 1/1.2816 = 0.78027465668, which is pretty long to type in. 
   
Read on if you would like to know a little bit more about the math
principle involved, namely, that multiplication of numbers has the
property of being "associative." The 2-step process is this: 
    
   Billed charge = (cost * 1.20) * 1.068     
   
where the parentheses show that the multiplication on the left is done 
first. The associative property of multiplication says that the result 
of a bunch of successive multiplications is going to be the same 
regardless of the way you associate the numbers together to indicate 
which multiplication is first, which is second, and so on. So, the 
formula above could be re-written as follows:  
   
   Billed charge = cost * (1.20 * 1.068) = cost * 1.2816  
   
This is nice because you can do the multiplication of the numbers that 
don't change only once this way, and not have to punch in two 
multiplications each time.  
   
I hope this helps.  
   
- Doctor Mike, The Math Forum
Check out our web site! http://mathforum.org/dr.math/