Calculate hours needed to balance account? - excel

Question

I have an accounts excel sheet where you input all your expenses, all your incomes (gst inclusive), and it calculates how you are placed (E.G. -$717.75 for the month).
I It also gives you the gst content to pay $taxableIncome*3)/23 and a rough guide as to how much income tax you should put away $taxableIncome*0.17.
You also tell the program what your hourly rate is.
I am wanting to add to the program to allow it to tell you that you need to work X more hours this month to balance.
This wouldn't be soo hard,
$deficit/$hourlyRate = hours needed to work except for each additional hour worked we need to add ($hourlyRate*3)/23 to the gst expense, and add $hourlyRate*0.17 to the income tax expense.
This is the part I don't quite get how to work out.
So given an hourly rate of $21.00+gst = $24.15/h and a deficit of $717.75 how can I work out how many more hours I would need to work?
basically I am wondering how I can do a formula of
0 <= [(x1+x2+x3...)-(y1+y2+y3...)] / z1
Where x1 must increase until the entire formula equals 0, but as x1 increases, so must y1 and y2
x. = Income Source
y. = Expense
z. = Hourly Rate (gst inclusive)
Note that while the excel formula would be useful I am not expecting people to do the work for me, just a generic overview in pseudocode will work.

Answer 1

So, set:
gross new wage incl. gst - new gst - new income tax) =
-(current income - current expense) or -(Y-E)
where -(Y-E) >= 0
gross new wage - (gross new wage * 3/23) - (gross new wage * 0.17) = -(Y-E)
gross new wage * (1 - 3/23 - 0.17) = -(Y-E)
gross new wage = -(Y-E) / (1 - 3/23 - 0.17)
new hours * gross wage rate (incl. gst) = -(Y-E) / (1 - 3/23 - 0.17)
new hours = (-(Y-E) / (1 - 3/23 - 0.17)) / gross wage rate
That works, doesn't it?