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 mealgebraicallyas 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