SOLUTION: When calculating his income tax an accountant realized that his federal tax was 30% of his income after his provincial tax was paid, and that his provincial tax was 20% of his inco

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Question 1097804: When calculating his income tax an accountant realized that his federal tax was 30% 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 $47 000, how much federal tax did he have to pay?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
his income is 47000.

his federal tax is 30% of (47000 minus his provincial tax).

his provincial tax is 20% of (47000 minus his federal tax).

let F equal his federal tax.
let P equal his provincial tax.

your equations are:

F = .3 * (47000 - P)
P = .2 * (47000 - F)

simplify these equations to get:

F = 14100 - .3P
P = 9400 - .2F

you have two equations that need to be solved simultaneously.

add .3 * P to both sides of the first equation and add .2 * F to both sides of the second equation to get:

F + .3P = 14100
.2F + P = 9400

leave the first equation as is and multiply both sides of the second equation by 5 to get:

F + .3P = 14100
F + 5P = 47000

subtract the first equation from the second to get:

4.7P = 32900

solve for P to get P = 32900 / 4.7 = 7000.

go back to your first original equation and solve for F to get:

F = .3 * (47000 - P) becomes F = .3 * (47000 - 7000)) which becomes F = .3 * 40000 which becomes F = 12000.

his federal tax is 12,000.
his provincial tax is 7,000.