Question 803156: I can't figure out the formula for the question: a painting is sold for $100 total. At 7.25% tax what does the seller now owe the state? The answer isn't $7.25 either.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! They probably mean that the buyer pays $100 including the 7.24% tax.
That would mean that the buyer pays 107.25% of the price of the painting,
with the seller getting 100% of the price of the painting,
and the state getting 7.25% of the price of the painting.
7.25% as a ratio and as a decimal is 
107.25% as a ratio and as a decimal is 
The price times  is the total that the buyer paid
The price was
$100 ÷ 1.0725 = $93.24,
and that is what the seller gets.
The state gets the remaining 
( $100 - $93.24 = $6.76 ),
which is 7.25% of $93.24.
We can verify by calculating 7.25% of $93.24
$93.24 times 0.0725 = $6.76
NOTES:
I get $6.76 after rounding the 6.7599 result,
but I also had to round the result of 100 ÷ 1.0725,
which was 93.24009324009324009324009234........
It was very clever of the seller to calculate the price as $93.24,
so that the total payment, with tax, would add up to an even $100.
That even $100 is very convenient for the buyer,
who probably does not know even know that the seller does not get to keep the whole $100.
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