An amazing amount of discussion, for an apparently trivial question.

About the only thing "proved" is that the first GUEST was wrong - for a bunch of musicians, it ain't that simple.

MudGuard's answer is correct. The only simplification I can see is to "reduce" the 1/(1+.065) to 0.93897. Multiply the amount "collected" by 0.93897 to get the "sale price." Then when the "sale price" is multiplied by 0.065, you get the tax. Add Price + Tax and you should come up with the amount collected ($100 for purposes of the original question.

The remaining difficulty is that various tax jurisdictions don't always come up with the "mathematically correct" number as the amount you must pay.

Many tax jurisdictions will permit you to pay a "lump sum" percentage of the total "amount of sales." Others insist that each item sold must be taxed separately, and you must pay the "total of the taxes collected on individual sales."

Some of these later bandits jurisdictions require "rounding up" on each individual sale. This can significantly increase the amount collected.

For information on North Carolina, you might want to check out:

Tax Forms and Instructions: North Carolina

From there, you can click to:

Sales and Use Taxes: North Carolina

The "real world answers" should be there(?).

John