total brain fart?

[01]

$100 pre-tax revenue is $10825 after tax.

Or,we can say that $108.25 with tax is $100 pre-tax

Therefore $546.25 with tax

=546.25*100/108.25

=$504.62 pre-tax

Suppose revenue with tax was $110 with a tax rate of 10%.

I'll bet you can guess the anwer to this one. I',m going to guess the revenue was $100. How could I check if my guess was correct? Just calculate the tax and add revenue and tax to see if they come to $110.

So let's check: 100 + 10% of 100 = 100+10 = $110. Looks like we got it.

Now your problem is not as easy to guess but the method is the same. The guess we always make in algebra is X:

Let X = the revenue. Then X + 8.25% of (X) = 546.25

or X + 0.0825X = 546.25 so 1.0825X=546.25 and dividing

by 1.0825 gives Revenue = X = 546.25/1.0825 = $504.62 to the nearest cent.

If the tax rate is 8.25%, that means the pre-tax revenue (which is considered to be 100%) has 8.25% added onto it. Which means that 108.25% of the pre-tax revenue, call it x, is determined to be 546.25. So what we want to do is set up an equation:

108.25% of x = 546.25. Convert to a decimal and we get:

1.0825*x = 546.25. Divide by the 1.0825 and we get:

x = 546.25 / 1.0825 = 504.62

So we assume that the pre-tax revenue is $504.62.

If the tax rate is 8.25%, that means the pre-tax revenue (which is considered to be 100%) has 8.25% added onto it. Which means that 108.25% of the pre-tax revenue, call it x, is determined to be 546.25. So what we want to do is set up an equation:

108.25% of x = 546.25. Convert to a decimal and we get:

1.0825*x = 546.25. Divide by the 1.0825 and we get:

x = 546.25 / 1.0825 = 504.62

So we assume that the pre-tax revenue is $504.62.

Does that help?

you must add 100% to the tax rate (here giving the figure 108.25%) and then divide by that, remembering that percent is out of 100 so the figure you would divide by would be 1.0825

So the answer to the above figures would be :

546.25 / 1.0825 = 504.62

I am british so I haven't included the $ signs, but the maths is the same whether you are using British pounds £ or American dollers $

Tax = .0825R, where R = revenue. So, R + .0825R = 546.25, or R = 546.25/1.0825 = 504.62

Name it x.

For instance if it's calculated in a year,

x-(x*8.25/100)=546.25

Then make x the subject of the formula.