Adding Tax and TipDate: 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/ |
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