SOLUTION: hen calculating his income tax an accountant realized that his federal tax was 40% of his income after his provincial tax was paid, and that his provincial tax was 20% of his incom

Question 1197386: hen calculating his income tax an accountant realized that his federal tax was 40% of his income after his provincial tax was paid, and that his provincial tax was 20% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $46 000, how much federal tax did he have to pay?
Answer by ikleyn(52775) (Show Source): You can put this solution on YOUR website!
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When calculating his income tax, an accountant realized that his federal tax was 40%
of his income after his provincial tax was paid, and that his provincial tax was 20%
of his income after his federal tax was paid.
If the accountant's income before taxes amounted to $46 000, how much federal tax did he have to pay?
~~~~~~~~~~~~~~~~~

Let F be the federal tax;  P be the provincial tax.


[1]  First sentence is "his federal tax was 40% of his income after his provincial tax was paid".

     It means that   F = 0.4*(46000-P).     (1)



[2]  Second sentence is "his provincial tax was 20% of his income after his federal tax was paid".

     It means that   P = 0.2*(46000-F).     (2)



[3]  Thus we have two equations for two unknown, so the problem is solvable.


     Since they ask about F, I substitute P from equation (2) into equation (1). I get

         F = 0.4*(46000 - 0.2*(46000-F).


     Simplify and find F

         F = 0.4*46000 - 0.4*0.2*46000 + 0.4*0.2*F

         F - 0.4*0.2F = 0.4*46000 - 0.4*0.2*46000

            0.92F     =  14720

                F     =  14720/0.92 = 16000.


ANSWER.  Federal tax was 16000.

Solved.

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