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%

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?

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.