[SOLVED] Find Base Total Amount

I believe this to be algebra problem that I have here, but I'm not positive. I'm not even sure that I can find this value mathematically, but I'm sure someone on this forum could tell me. Here is what I need to know:

If I have a base amount of $30 and a final amount of $30.70. I need to know how much of the base amount has been paid for and how much of the .70 tax was paid for.

Example:

$10 is taxable at 7%
$20 is NOT taxable
------------------
$30 Base Total

If I have this equation here:
$30.70 = $20 + ($10+($10 * 7%))

An individual only pays for $10.50.

How do I find how much of the Base amount is left?
$30 - (Portion of payment that is base amount)=Base Amount Left

How do I find how much of the tax total is left?
.70 - (Portion f paymen that is tax)=Tax Amount Left

I am not sure if I understand your question?

Are you saying someone has $30, and there is a 7% tax bracket for the first $10, and 0% on the rest?

That gives us in taxes

If the tax bracket is up to $10.50, then taxes are equal to or 73.5 cents in taxes.

Thank you for the quick reply. Let me give you the exact scenario I need this for.

This is for an auction business. A buyer may buy 2 items. One for $20 and another for $10. The auction company only charges tax on the $10. The $20 does not have tax because it is "non taxable".

There is a buyers premium fee if someone pays with a credit card on the "base amount remaining". There is no fee if a buyer uses cash. So if the buyer pays $10.50 in cash, and the rest on the credit card. I need to know how much of the "base amount" is left so that the credit card premium will ONLY be charged on the "base amount remaining". A portion of the amount paid will pay for a portion of the .70 in tax and the other portion will pay for some of the base amount. I need to know what those portions are so the credit card premium is only figured on the base amount remaining and not the remaining tax.

Let me know if I can elaborate more on this.

Let me simply this. If I have $20 at 7% tax, I get a total of $21.40. If I use this equation:

$21.40/1.07 = $20, it will give me by base amount before the tax was added on.

What I need to know is if I have ($10 + ($10 + (10 * 7%))), I get a total of $20.70. How do I find out what the base amount of this is? I cant use $20.70/1.07 to get my base amount of $20 because only $10 of it is figured at the 7% rate. I need to know if there is a way to get the base amount om this scenario?

I am opening a new thread. One that isn't so confusing.