Formula to Calculate Back and Forth Between Net & Gross Based on Markup Percentage

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I'm trying to develop a cost management spreadsheet for my company. The way we currently manage budgets is by taking the total budget from the proposal (Gross), subtracting our cut, then getting the monthly spend (Net).

At the end of the month, we then go in and input the actual spend for that month (Net) and bill clients based on actual spend + our cut (Gross).

So I essentially need to be able to calculate from Gross to Net, then back to Gross. I've got formulas that work backward and forward - but they don't calculate out to match what calculates in this Markup Calculator: https://www.omnicalculator.com/business/markup

If Gross = G, Net = N, Markup = M

I've got:

G = N+(N*M)/100

But when I try to work that backward, I get all screwed up. I'm writing:

N = G-(G*M)/100

https://docs.google.com/spreadsheets/d/19NKX2m8wRoAhkX4Ns-rO26cszM2tY-STwfvjlltpiSY/edit?usp=sharing

I'm horrific at math - so feel free to dumb it down as much as possible!

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$$G=N+\frac {NM}{100}\\G=N\left(1+\frac M{100}\right)\\\frac G{1+\frac M{100}}=N$$