# Basic math calculation

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• Aug 5th 2011, 05:39 PM
dwat
Basic math calculation
I'm doing a problem that's are tax inclusive & exclusive. Finding tax.

Doing a basic example involving $100 including tax. tax rate is 15%. I was taught at school this method.$\displaystyle 100 - 15 = 85\displaystyle .85 * 100 = 85$and therefore tax is$15.

Then $85 (excluding tax). If I wanted to go back to tax inclusive you add 15% on top of cost price. Therefore,$\displaystyle 85 * 1.15 = 97.75$It doesn't come back to the correct amount tax inclusive of$100.

WHY?

Here is the proper calculation formula I was given to use. 100 * (3/23)

and yes that method is right.

Because that method is correct, can anyone explain to me algebraically as to how they derived the formula: Price (tax inclusive) * (3/23) based on a 15% tax rate and why isn't my old method not correct?

Thanks
• Aug 5th 2011, 05:58 PM
BERMES39
Re: Basic math calculation
An item M plus 15% tax is $100. M(1+0.15) = M*1.15 = 100 M = 100/1.15 = 86.95 (not 85) The fraction 3/23 only works for 15% • Aug 5th 2011, 11:37 PM Bacterius Re: Basic math calculation It's because 15% of$100 is not the same amount as 15% of $85. To reverse the tax, and thus reverse the multiplication by 0.85, you must multiply by$\displaystyle \frac{1 }{0.85}$which turns out to be 1.17647 rounded, not quite 1.15. Which explains why you don't get the$100 total back.

Now note that $\displaystyle \frac{3}{23} = \frac{15}{115}$, can you notice something?
• Aug 6th 2011, 01:30 AM
HallsofIvy
Re: Basic math calculation
As Bacterius said, with percents you always have to consider the "base". The tax on a purchase is 15% of the price without the tax added, then add the tax to get the price with tax. Here, you do not know, but want to find, the purchase price without the tax. If we call that price "P", the we have 15% of P or 0.15P. To find the price with the the tax, add P and 0.15P: P+ 0.15P= (1+ 0.15)P= 1.15P. You are told that the price "including tax" is \$100 so you have 1.15P= 100. You can find the price without tax by dividing both sides by 1.15.