SOLUTION: When calculating his income tax an accountant realized that his federal tax was 25% of his income after his provincial tax was paid, and that his provincial tax was 15% of his inco

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Question 1204269: When calculating his income tax an accountant realized that his federal tax was 25% of his income after his provincial tax was paid, and that his provincial tax was 15% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $120 000, how much federal tax did he have to pay (to the nearest penny)?
Answer by ikleyn(52788) About Me  (Show Source):
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When calculating his income tax an accountant realized that his federal tax was 25%
of his income after his provincial tax was paid, and that his provincial tax was 15%
of his income after his federal tax was paid. If the accountant's income before taxes
amounted to $120 000, how much federal tax did he have to pay (to the nearest penny)?
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Let F be the federal tax amount;
let P be the provincial tax amount.


Write equations as you read the problem

    F = 0.25*(120000 - P)      (1)   "federal tax was 25% of his income after his provincial tax was paid"

    P = 0.15*(120000 - F)      (2)   "provincial tax was 15% of his income after his federal tax was paid"


This system is ready to be solved by substitution - so, substitute P from equation (2) into equation (1).
You will get then

    F = 0.25*120000 - 0.25*0.15*(120000-F).


Simplify and find F

    F = 30000 - 0.0375*120000 + 0.0375*F

    F - 0.0375F = 30000 - 0.0375*120000

      0.9625F   =     25500

           F   =     25500/0.9625 = 26493.51  (to the nearest cent)

           P = 0.15*(120000 - 26493.51) = 14025.97  (to the nearest cent)


ANSWER.  Federal tax is  26493.51.   Provincial tax is  14025.97.

Solved.