Simple real life problem

Question

Let say my girlfriend makes $2000$ Euros per month and I make $3400$ Euros, let say all our living costs sum up to $1540$ Euros. How can i calculate how much each of us must pay (off the $1540$ Euros) so as our participation is proportional to our income?

Thanks

Answer 1

Your net income per month is 5400 euros so since she make 2000 euros that is 37% of your total income so she should pay 37% of your total expenses. $1540*.37 = 570.37$ per month as her portion of the expenses your portion would be $3400/5400 = .63$, $ 1540*.63 = 969.62 $. If you sum the two together you can then see it works out $570.37 + 969.62 = 1539.99$ ( 1 cent got lost to rounding).

Answer 2

Write down the equations that must be satisfied. Let $x$ be the amount you pay and $y$ the amount your girlfriend pays.

One equation is simple: $x+y=1540$, since you must pay the whole costs. The other equation comes from the proportions that must be satisfied:

$$x:y = 3400 : 2000$$ Which can also be written as $$\frac xy = \frac{3400}{2000}$$

Answer 3

The total income is $2000 + 3400 = 5400$ euros. Since your girlfriend makes only $2000$ euros (sexist!), she makes $\frac{2000}{5400} = .37...$ (roughly $37 \% $) of the income, which means she should only pay $37 \% $ of the rent.

Then, she should only pay $1540 *.37 = 569.80 $ euros, roughly.