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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(52790)   (Show Source):
You can put this solution on YOUR website! .
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.
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