# Thread: This should not be difficult, but I can't figure it out

1. ## This should not be difficult, but I can't figure it out

My girlfriend and I are trying to figure out how to divide costs in such a way that we both end up paying the same percentage of our income on each expense, but both of us are very math challenged and can't figure out how to do this. To clarify, let's say I make 2500 per month, and she makes 2000. Rent is 1000 (50% of her income, and 40% of mine). How do we split the cost of rent in such a way that it ends up being the same percentage of our monthly income? We are trying to come up with a formula that we can enter into excel and have it calculate the amount each of us has to pay for each bill. Any help would be greatly appreciated.

2. ## Re: This should not be difficult, but I can't figure it out

if your total income is x and your total bills are y. Then you can get the outcome you want if you each spend a proportion $\displaystyle \frac{y}{x}$ of your income.

in this case $\displaystyle x=2000 + 2500 = 4500$
in this case $\displaystyle y=1000$

so $\displaystyle \frac{y}{x} = \frac{1000}{4500} = 0. \dot{2} \dot{2}$

You pay $\displaystyle 2500 \times \frac{1000}{4500} = 444.444444...$
She pays $\displaystyle 2000 \times \frac{1000}{4500} = 555.5555555...$

You will presumably have to round to 1 cent at some point, eg she pay 444.45 and you pay 555.55. Or she could pay 444.44 and you pay 555.56.

3. ## Re: This should not be difficult, but I can't figure it out

Originally Posted by SpringFan25
if your total income is x and your total bills are y. Then you can get the outcome you want if you each spend a proportion $\displaystyle \frac{y}{x}$ of your income.

in this case $\displaystyle x=2000 + 2500 = 4500$
in this case $\displaystyle y=1000$

so $\displaystyle \frac{y}{x} = \frac{1000}{4500} = 0. \dot{2} \dot{2}$

You pay $\displaystyle 2500 \times \frac{1000}{4500} = 444.444444...$
She pays $\displaystyle 2000 \times \frac{1000}{4500} = 555.5555555...$

You will presumably have to round to 1 cent at some point, eg she pay 444.45 and you pay 555.55. Or she could pay 444.44 and you pay 555.56.
Thank you so much for the help. I think I failed to explain the issue properly, however. In your example, I end up paying less than she does, which does not make sense since I make more money. Presumably, in order for us to spend the same percentage of our separate income, I would have to pay more (since 1000 is only 40% of my income), and she would have to pay less (since 1000 is 50% of her income). Does that make sense?

Thanks again for the help.

4. ## Re: This should not be difficult, but I can't figure it out

Originally Posted by dyslexicnumbers
My girlfriend and I are trying to figure out how to divide costs in such a way that we both end up paying the same percentage of our income on each expense, but both of us are very math challenged and can't figure out how to do this. To clarify, let's say I make 2500 per month, and she makes 2000. Rent is 1000 (50% of her income, and 40% of mine). How do we split the cost of rent in such a way that it ends up being the same percentage of our monthly income? We are trying to come up with a formula that we can enter into excel and have it calculate the amount each of us has to pay for each bill. Any help would be greatly appreciated.
Let's say your salary is S, her salary is T, the amount of the rent is R, and the fraction you each pay of your salaries is f. Then we must have

$\displaystyle fS + fT = R$

so

$\displaystyle f = \frac{R}{S+T}$

The amount you pay is
$\displaystyle fS = \frac{RS}{S+T}$

and the amount she pays is
$\displaystyle fT = \frac{RT}{S+T}$

With the values you gave, this works out to 555.55 for you and 444.44 for her.

5. ## Re: This should not be difficult, but I can't figure it out

total income = 4500

to keep it simple, you make about 55% of the total income, she makes 45%

you should pay 55% of the rent = $550 she pays 45% =$450

this works out so that 22% of your income goes toward rent, and 22.5% of her income goes to rent.

so, treat her to a nice dinner every month and call it square.

6. ## Re: This should not be difficult, but I can't figure it out

Originally Posted by awkward
Let's say your salary is S, her salary is T, the amount of the rent is R, and the fraction you each pay of your salaries is f. Then we must have

$\displaystyle fS + fT = R$

so

$\displaystyle f = \frac{R}{S+T}$

The amount you pay is
$\displaystyle fS = \frac{RS}{S+T}$

and the amount she pays is
$\displaystyle fT = \frac{RT}{S+T}$

With the values you gave, this works out to 555.55 for you and 444.44 for her.
Thank you so much! This does exactly what we need. I'm so embarrassed that we were unable to figure it out by ourselves.