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(52772)   (Show Source):
You can put this solution on YOUR website! .
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?
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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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