MudGuard's explanation is correct. IvanB's figures are correct.
GUEST at 24-Feb-02 - 06:12 PM, John Routledge, and Nathan (harpgirl's post) were wrong. Problem stated that selling price INCLUDING tax was 100, thus "item price + 6.5% of item price = 100". Whatever item price is, it is NOT 100, and thus 6.5% of item price is NOT 6.5.
AR282's reply is wrong if he uses MudGaurd's definition of "selling price" (item price plus tax). It could be considered technically correct if he means the pre-tax price of the item, but is then useless in solving the problem--we already know how to figure the tax given the item price, the question is how to figure the item price.
To sum it up in algebra:
P = item price, what we're trying to calculate
S = amount of sale (MudGaurd's "selling price"), which includes item price plus tax, which is 6.5% of item price
S is known to be 100. What is P?
S = P + 6.5%P = 100
S = 1.065P = 100
1.065P = 100
P = 100/1.065 = 93.90 (rounded to second decimal place)
Double check (all figures rounded to second decimal place):
93.90 + 6.5%(93.90) = 93.90 + 6.10 = 100
Figures add up, all is well.