Real Life Rounding Phenomena When Solving for Variables I have a question that I've been thinking a long time about without being able to come up with an answer and would appreciate some help:
I am attempting to subtract two distinct fees from a total transaction, depending on transaction price.
Fee #1 = 2.9% of transaction price
Fee #2 = 10% of transaction price
Let T = transaction price.  Therefore :
Let F = Total Fees
F = T(0.029) + T(0.1)
F = T(0.129)
F / 0.129 = T
This seems to look ok, HOWEVER, in the real world, each fee is rounded to the nearest cent.  So, for Fee #1, assuming a transaction price of 10.99, the fee would be 0.31871 and thus rounded to 0.32.  This would give a slightly different result from the algebraic result, given this rounding phenomenon.
My question is, in equations such as the one in the example, is there a way to account for  discrete rounding of terms before solving for a variable?

How about multiplying by a factor $c$ first, then dividing the final answer by the same factor again?
For $f_1=$ fee #1, $f_2=$ fee #2, $c = 10$.
$$F\cdot c = T(f_1 \cdot c) + T(f_2 \cdot c) = T((f_1+f_2)\cdot c)$$
$$F = \frac{T((f_1+f_2)\cdot c)}{c}$$
Of course you solve the parentheses and numerator first. You can use bigger values of $c$ if you need more accuracy. e.g. $c=100, 1000, \ldots$.
