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I'm trying to make a spreadsheet to split the house bills with my SO. I want to split the bills accordingly to our income so (the values are dummy) incomeA = 1000; incomeB = 600; percA = incomeA / (incomeA + incomeB); (0.625) percB = incomeB / (incomeA + incomeB); (0.375)

This is "our 50/50" and, in most of the bills is ok. If we have a bill of 40, I will play 25 (40 * 0.625) and she will pay 15 (40 * 0.375).

Now, let's say that we have a bill that I want to pay more than the "our 50/50" (75/25, for example) How can I translate our 50/50 ratio into that 75/25?

I don't really know how to put this in better words. Thanks in advance

Bruno Camarneiro
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    How about setting a multiplier to both 'incomeA' and 'incomeB'? The 50/50 you mention would set 'incomeA=10000.5=500' (the same for 'incomeB'). For the 75/25, 'incomeA=10000.75=750' (and similar for 'incomeB'). Good enough to get the percentages 'percA' and 'percB'. Now, I am not sure this is what you are asking. – DavidPM Nov 30 '18 at 16:56
  • @DavidPM yes! That works! Thanks! can you add that comment as an answer so I can accept it? – Bruno Camarneiro Nov 30 '18 at 17:17

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For a simple solution, we set a multiplier (say $\lambda_1$) to incomeA and another one (say $\lambda_2$) to incomeB, in a way that $\lambda_1+\lambda_2=1$ (or $100$ if it results more intuitive).

In the case of the 75/25 ratio you mention in your example, we would set

$$\text{incomeA} = 1000*\lambda_1=1000*0.75$$ $$\text{incomeB} = 600*\lambda_2=600*0.25$$

We would do the same for the 50/50 example, with $\lambda_1=\lambda_2=0.5$.

The true amounts of incomeA and incomeB do not really matter since we are mostly interested in getting the percentages percA and percB.

DavidPM
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