Sales Tax Total and % is known what is the cost of goods.

Question

My question is. The sale tax is 8.6 % the total cost of the item including sales tax is $ 65.61. What is the formula to find the cost of the actual item ?

Answer 1

The way I'm interpreting this is

$Cost of Item + Sales Tax = 65.51$.

In that case, all you represent the original cost of the item as $x$. Therefore

$x + x*SalesTax = TotalCost$.

So all you need to do is turn the percentage into a decimal. 8.6% = .086.
Which gives you $x +.086*x = 65.61$ This simplifies to $1.086x = 65.61$ or $x = 60.41$. The simpler formula is just that

$Orginal Cost / (1 + SalesTax) = Orginal Cost$

or $65.61 / 1.086 = OrginalCost$ which again is $60.41.

Answer 2

If $x$ is the cost of the item, then the cost plus tax is

$$x + 0.086x = x(1.086).$$

That should be equal to the final cost, so

$$x(1.086) = 65.61.$$

If $r$ is the tax rate, then you have $(1+r)\mbox{cost} = \mbox{final}.$