Seb's salary is $X per annum. The tax system is such that Seb pays a 15% flat rate of income tax on his salary. The tax system is due for reform, and politicians have suggested the following:
1. Any income under $12,000 should be tax free.
2. Anything above $12,000 should be taxed at 25%.
Given that Seb will be paying $1,500 more under the new system, calculate how much tax Seb pays under the current system. You can assume that X>$12,000.

To find X, we use the fact that the amount of tax under the old system, increased by $1,500 will give the amount of tax payable under the new system, so we can form an equation for X as follows:

15%×X+1,500=25%×(X−12,000),

i.e.

0.15X+1,500=0.25×(X−12,000),

giving

0.15X+1,500=0.25X−3,000,

Getting X on one side gives

4,500=0.1X,

and solving for X gives

45,000=X.

So, X=$45,000.

martinragetv martinragetv · Answer 2 · 2022-06-12T08:56:18+02:00

Answer:

$6,750

Step-by-step explanation:

To find X, we use the fact that the amount of tax under the old system, increased by $1,500 will give the amount of tax payable under the new system, so we can form an equation for X as follows:

15%×X+1,500=25%×(X−12,000),

that is

0.15X+1,500=0.25×(X−12,000),

giving

0.15X+1,5004,500X=0.25X−3,000=0.10X=45,000

which solves to give X=$45,000. Therefore, under the current system Seb pays

Tax (Current System)=$45,000×15%=$6,750.

Check the tax under the new system too. We have

Tax (Proposed System)=$(45,000−12,000)×25%=$8,250,

and we note that $8,250−$6,750=$1,500.