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

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) (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)?
~~~~~~~~~~~~~~~~~~~~

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.

RELATED QUESTIONS
When calculating his income tax an accountant realized that his federal tax was 40% of... (answered by ikleyn)

When calculating his income tax an accountant realized that his federal tax was 30% of... (answered by Theo)

hen calculating his income tax an accountant realized that his federal tax was 40% of his (answered by ikleyn)

When calculating his income tax an accountant realized that his federal tax was 25% of... (answered by Theo)

An employee pays an income tax of P12,210.00 on his gross income of P146,520.00. What is... (answered by ewatrrr)

An employee pays an income tax of P12,210.00 on his gross income of P146,520.00. What is... (answered by rfer)

If a man pays Rs 2500 as income tax; that is 50% of his total income;then what will be... (answered by fractalier)

When saled used the tax table to calculate his income tax payable, it turned out to be... (answered by greenestamps)

Alex, a resident of Metropolis, pays Metropolis an annual tax of $32 plus 2.6% of his... (answered by scott8148)