Question 408716
Amount of taxes payed on $125000 is federal 50% and state 30%. The federal tax is computed after state tax paid. The state tax is computed after federal tax is paid. How much is the federal and state taxes?

Solution: Let y be the total income
Therefore, State Tax= y x 30%
                    =30y/100
                    =3y/10
Income after State Tax = y - 3y/10
                       = 7y/10

Now, Federal Tax= 7y/10 x 50%
                 = 7y/20

so total tax= 3y/10 + 7y/20

Now this total tax must be equal to 125000
Therefore,
3y/10 +  7y/20 = 125000
(6y + 7y)/20 = 125000
13y/20 = 125000
so, y = (125000 x 20)/13
    y= $192307.69
State Tax= $192307.69 x 30%
         =$ 57692.31
Income after state tax= $192307.69 - $ 57692.31
                      = $ 134615.38
So, Federal Tax = $134615.38 x 50%
                 = $ 67307.69