SOLUTION: 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 25% of his inco

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Question 1208619: 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 25% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $180000, how much federal tax did he have to pay?
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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 25% of his income after his federal tax was paid. If the accountant's income before taxes amounted
to $180000, how much federal tax did he have to pay?
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Let F be the federal tax amount, in follars;

let P be the provincial tax, in dollars.


From the problem, we have these two equations

    F = 0.4*(180000 - P),     (1)

    P = 0.25*(180000-F).     (2)


Substitute expression for P from equation (2) into equation (1)

    F = 0.4*(180000-0.25*(180000-F)).     (3)


You have an equation for single unknown F.  Simplify it and find F

    F = 0.4*180000 - 0.4*0.25*(180000-F)

    F = 72000 - 0.1*(180000-F)

    F = 72000 - 18000 + 0.1F

    F - 0.1F = 72000- 18000

       0.9F    =     54000

            F    =      54000/0.9 = 60000.


At this point, the problem is solved completely.


ANSWER.  The federal tax was $60,000.

Solved.