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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

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????).

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/
```
Associated Topics:
Elementary Fractions
Elementary Multiplication
Middle School Fractions
Middle School Ratio and Proportion

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